Abstract group data - 1152.155815

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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, 3, 4, 2, 12, 2, 3, 12, 2, 2], 'aut_gens': [[1, 2, 4, 96, 192], [385, 658, 676, 576, 288], [1, 2, 52, 96, 960], [1, 34, 4, 576, 288], [817, 18, 164, 672, 960], [1, 98, 580, 96, 192], [841, 170, 764, 96, 288], [1, 98, 100, 96, 192], [385, 2, 4, 96, 192], [433, 690, 620, 672, 192], [1, 2, 20, 96, 288], [1, 2, 20, 96, 1056]], 'aut_group': '4608.lj', 'aut_hash': 3301011005301566777, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 40, 'aut_perms': [222878310242743093851036800049314336396184227829, 34235912619974656449121003151047472, 274262421130446403236171082112728910219504920633, 703958657288525955173774089601128573461545261151, 640287607978924088499899587622905767850192992021, 374384514948145003625475088332392388622269019165, 69284399697161295877193405532126334653399283, 1865928055624373176227083973959528, 642682759127218945480843315206636520337796249324, 274097245674440001024482904571230256027317384324, 274097245674440001024483033831659678545142492940], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 1], [2, 24, 1, 2], [2, 36, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 4], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 48, 1, 2], [6, 96, 1, 1], [8, 4, 1, 1], [8, 12, 1, 1], [8, 72, 1, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 48, 1, 2], [12, 96, 1, 1], [24, 4, 2, 1], [24, 12, 2, 1], [24, 16, 2, 1], [24, 16, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '576.8659', 'autcentquo_hash': 8659, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2:D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 1], [2, 24, 2], [2, 36, 2], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 2, 1], [4, 6, 1], [4, 12, 1], [4, 24, 2], [4, 36, 4], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 16, 1], [6, 48, 2], [6, 96, 1], [8, 4, 1], [8, 12, 1], [8, 72, 2], [12, 4, 1], [12, 12, 1], [12, 16, 3], [12, 48, 2], [12, 96, 1], [24, 4, 2], [24, 12, 2], [24, 16, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '576.8314', 'commutator_count': 1, 'commutator_label': '144.155', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 155815, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 1], [2, 24, 1, 2], [2, 36, 1, 2], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 36, 1, 4], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 48, 1, 2], [6, 96, 1, 1], [8, 4, 1, 1], [8, 12, 1, 1], [8, 72, 1, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 16, 2, 1], [12, 48, 1, 2], [12, 96, 1, 1], [24, 4, 2, 1], [24, 12, 2, 1], [24, 16, 2, 1], [24, 16, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 80640, 'exponent': 24, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '288.1028', 'hash': 155815, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 12, 2, 6], 'inner_gens': [[1, 2, 76, 96, 960], [1, 2, 92, 96, 288], [25, 10, 4, 576, 288], [1, 2, 676, 96, 192], [385, 98, 100, 96, 192]], 'inner_hash': 8314, 'inner_nilpotent': False, 'inner_order': 576, 'inner_split': True, 'inner_tex': 'D_{12}:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 10], [3, 8], [4, 15], [6, 6], [12, 4]], 'label': '1152.155815', 'linC_count': 48, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 32, 'linQ_dim': 9, 'linQ_dim_count': 32, 'linR_count': 96, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C24:(C2*S4)', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 51, 'number_divisions': 44, 'number_normal_subgroups': 49, 'number_subgroup_autclasses': 596, 'number_subgroup_classes': 616, 'number_subgroups': 6310, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 139], [3, 26], [4, 212], [6, 230], [8, 160], [12, 256], [24, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[49, 2, 4, 96, 192], [1, 2, 4, 96, 960], [1, 2, 68, 96, 288]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [3, 8], [4, 5], [6, 6], [8, 3], [12, 2], [16, 1], [24, 1]], 'representations': {'PC': {'code': '1526828714687060281222831248043656438401775070021718954885609123694425179764745', 'gens': [1, 2, 3, 7, 8], 'pres': [9, -2, -2, -2, -2, -2, -3, -2, 2, -3, 2054, 1253, 74, 2019, 1596, 102, 1813, 130, 1742, 9096, 5325, 2310, 1374, 69127, 10384, 5209, 7810, 1339, 1996, 214, 62216]}, 'Perm': {'d': 15, 'gens': [21156670200, 27393851525, 94486734720, 194166604800, 295076597760, 3, 840, 7, 16]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:(C_2\\times S_4)', 'transitive_degree': 72, '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: 108500882
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 155815, 'group_order': 1152, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 108500893
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 155815, 'group_order': 1152, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 48, 'size': 1}
  • id: 108500904
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 3, 'group_counter': 155815, 'group_order': 1152, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 624, 'size': 3}
  • id: 108500915
    {'aut_label': '2C', 'centralizer': '3.b1.a1', 'counter': 4, 'group_counter': 155815, 'group_order': 1152, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 576, 'size': 3}
  • id: 108500926
    {'aut_label': '2D', 'centralizer': '12.bm1.a1', 'counter': 5, 'group_counter': 155815, 'group_order': 1152, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 385, 'size': 12}
  • id: 108500929
    {'aut_label': '2E', 'centralizer': '24.d1.a1', 'counter': 6, 'group_counter': 155815, 'group_order': 1152, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 26, 'size': 24}
  • id: 108500930
    {'aut_label': '2F', 'centralizer': '24.p1.a1', 'counter': 7, 'group_counter': 155815, 'group_order': 1152, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 46, 'size': 24}
  • id: 108500931
    {'aut_label': '2G', 'centralizer': '36.d1.a1', 'counter': 8, 'group_counter': 155815, 'group_order': 1152, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 227, 'size': 36}
  • id: 108500932
    {'aut_label': '2H', 'centralizer': '36.bh1.a1', 'counter': 9, 'group_counter': 155815, 'group_order': 1152, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 961, 'size': 36}
  • id: 108500883
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 10, 'group_counter': 155815, 'group_order': 1152, 'label': '3A', 'order': 3, 'powers': [10, 1], 'representative': 384, 'size': 2}
  • id: 108500884
    {'aut_label': '3B', 'centralizer': '8.j1.a1', 'counter': 11, 'group_counter': 155815, 'group_order': 1152, 'label': '3B', 'order': 3, 'powers': [11, 1], 'representative': 32, 'size': 8}
  • id: 108500885
    {'aut_label': '3C', 'centralizer': '16.k1.a1', 'counter': 12, 'group_counter': 155815, 'group_order': 1152, 'label': '3C', 'order': 3, 'powers': [12, 1], 'representative': 800, 'size': 16}
  • id: 108500886
    {'aut_label': '4A', 'centralizer': '2.g1.a1', 'counter': 13, 'group_counter': 155815, 'group_order': 1152, 'label': '4A', 'order': 4, 'powers': [2, 13], 'representative': 24, 'size': 2}
  • id: 108500887
    {'aut_label': '4B', 'centralizer': '6.u1.a1', 'counter': 14, 'group_counter': 155815, 'group_order': 1152, 'label': '4B', 'order': 4, 'powers': [2, 14], 'representative': 648, 'size': 6}
  • id: 108500888
    {'aut_label': '4C', 'centralizer': '12.bw1.a1', 'counter': 15, 'group_counter': 155815, 'group_order': 1152, 'label': '4C', 'order': 4, 'powers': [2, 15], 'representative': 397, 'size': 12}
  • id: 108500889
    {'aut_label': '4D', 'centralizer': '24.f1.a1', 'counter': 16, 'group_counter': 155815, 'group_order': 1152, 'label': '4D', 'order': 4, 'powers': [4, 16], 'representative': 706, 'size': 24}
  • id: 108500890
    {'aut_label': '4E', 'centralizer': '24.bl1.a1', 'counter': 17, 'group_counter': 155815, 'group_order': 1152, 'label': '4E', 'order': 4, 'powers': [4, 17], 'representative': 590, 'size': 24}
  • id: 108500891
    {'aut_label': '4F', 'centralizer': '36.bm1.a1', 'counter': 18, 'group_counter': 155815, 'group_order': 1152, 'label': '4F', 'order': 4, 'powers': [2, 18], 'representative': 637, 'size': 36}
  • id: 108500892
    {'aut_label': '4G', 'centralizer': '36.g1.a1', 'counter': 19, 'group_counter': 155815, 'group_order': 1152, 'label': '4G', 'order': 4, 'powers': [4, 19], 'representative': 1059, 'size': 36}
  • id: 108500894
    {'aut_label': '4H', 'centralizer': '36.q1.a1', 'counter': 20, 'group_counter': 155815, 'group_order': 1152, 'label': '4H', 'order': 4, 'powers': [2, 20], 'representative': 859, 'size': 36}
  • id: 108500895
    {'aut_label': '4I', 'centralizer': '36.bc1.a1', 'counter': 21, 'group_counter': 155815, 'group_order': 1152, 'label': '4I', 'order': 4, 'powers': [3, 21], 'representative': 187, 'size': 36}
  • id: 108500896
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 22, 'group_counter': 155815, 'group_order': 1152, 'label': '6A', 'order': 6, 'powers': [10, 2], 'representative': 432, 'size': 2}
  • id: 108500897
    {'aut_label': '6B', 'centralizer': '6.p1.a1', 'counter': 23, 'group_counter': 155815, 'group_order': 1152, 'label': '6B', 'order': 6, 'powers': [10, 3], 'representative': 240, 'size': 6}
  • id: 108500898
    {'aut_label': '6C', 'centralizer': '6.p1.a1', 'counter': 24, 'group_counter': 155815, 'group_order': 1152, 'label': '6C', 'order': 6, 'powers': [10, 4], 'representative': 192, 'size': 6}
  • id: 108500899
    {'aut_label': '6D', 'centralizer': '8.j1.a1', 'counter': 25, 'group_counter': 155815, 'group_order': 1152, 'label': '6D', 'order': 6, 'powers': [11, 2], 'representative': 16, 'size': 8}
  • id: 108500900
    {'aut_label': '6E', 'centralizer': '16.k1.a1', 'counter': 26, 'group_counter': 155815, 'group_order': 1152, 'label': '6E', 'order': 6, 'powers': [12, 2], 'representative': 400, 'size': 16}
  • id: 108500901
    {'aut_label': '6F', 'centralizer': '48.g1.a1', 'counter': 27, 'group_counter': 155815, 'group_order': 1152, 'label': '6F', 'order': 6, 'powers': [10, 6], 'representative': 410, 'size': 48}
  • id: 108500902
    {'aut_label': '6G', 'centralizer': '48.h1.a1', 'counter': 28, 'group_counter': 155815, 'group_order': 1152, 'label': '6G', 'order': 6, 'powers': [10, 7], 'representative': 814, 'size': 48}
  • id: 108500903
    {'aut_label': '6H', 'centralizer': '96.e1.a1', 'counter': 29, 'group_counter': 155815, 'group_order': 1152, 'label': '6H', 'order': 6, 'powers': [11, 5], 'representative': 1025, 'size': 96}
  • id: 108500905
    {'aut_label': '8A', 'centralizer': '4.f1.a1', 'counter': 30, 'group_counter': 155815, 'group_order': 1152, 'label': '8A', 'order': 8, 'powers': [13, 30], 'representative': 12, 'size': 4}
  • id: 108500906
    {'aut_label': '8B', 'centralizer': '12.e1.a1', 'counter': 31, 'group_counter': 155815, 'group_order': 1152, 'label': '8B', 'order': 8, 'powers': [13, 31], 'representative': 588, 'size': 12}
  • id: 108500907
    {'aut_label': '8C', 'centralizer': '72.be1.a1', 'counter': 32, 'group_counter': 155815, 'group_order': 1152, 'label': '8C', 'order': 8, 'powers': [14, 32], 'representative': 279, 'size': 72}
  • id: 108500908
    {'aut_label': '8D', 'centralizer': '72.bf1.a1', 'counter': 33, 'group_counter': 155815, 'group_order': 1152, 'label': '8D', 'order': 8, 'powers': [13, 33], 'representative': 47, 'size': 72}
  • id: 108500909
    {'aut_label': '12A', 'centralizer': '4.f1.a1', 'counter': 34, 'group_counter': 155815, 'group_order': 1152, 'label': '12A', 'order': 12, 'powers': [22, 13], 'representative': 840, 'size': 4}
  • id: 108500910
    {'aut_label': '12B', 'centralizer': '12.e1.a1', 'counter': 35, 'group_counter': 155815, 'group_order': 1152, 'label': '12B', 'order': 12, 'powers': [22, 14], 'representative': 216, 'size': 12}
  • id: 108500911
    {'aut_label': '12C', 'centralizer': '16.k1.a1', 'counter': 36, 'group_counter': 155815, 'group_order': 1152, 'label': '12C', 'order': 12, 'powers': [25, 13], 'representative': 8, 'size': 16}
  • id: 108500912
    {'aut_label': '12D1', 'centralizer': '16.k1.a1', 'counter': 37, 'group_counter': 155815, 'group_order': 1152, 'label': '12D1', 'order': 12, 'powers': [26, 13], 'representative': 776, 'size': 16}
  • id: 108500913
    {'aut_label': '12D1', 'centralizer': '16.k1.a1', 'counter': 38, 'group_counter': 155815, 'group_order': 1152, 'label': '12D-1', 'order': 12, 'powers': [26, 13], 'representative': 472, 'size': 16}
  • id: 108500914
    {'aut_label': '12E', 'centralizer': '48.n1.a1', 'counter': 39, 'group_counter': 155815, 'group_order': 1152, 'label': '12E', 'order': 12, 'powers': [24, 16], 'representative': 514, 'size': 48}
  • id: 108500916
    {'aut_label': '12F', 'centralizer': '48.o1.a1', 'counter': 40, 'group_counter': 155815, 'group_order': 1152, 'label': '12F', 'order': 12, 'powers': [24, 17], 'representative': 302, 'size': 48}
  • id: 108500917
    {'aut_label': '12G', 'centralizer': '96.t1.a1', 'counter': 41, 'group_counter': 155815, 'group_order': 1152, 'label': '12G', 'order': 12, 'powers': [25, 15], 'representative': 989, 'size': 96}
  • id: 108500918
    {'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 42, 'group_counter': 155815, 'group_order': 1152, 'label': '24A1', 'order': 24, 'powers': [34, 30], 'representative': 420, 'size': 4}
  • id: 108500919
    {'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 43, 'group_counter': 155815, 'group_order': 1152, 'label': '24A-1', 'order': 24, 'powers': [34, 30], 'representative': 396, 'size': 4}
  • id: 108500920
    {'aut_label': '24B1', 'centralizer': '12.e1.a1', 'counter': 44, 'group_counter': 155815, 'group_order': 1152, 'label': '24B1', 'order': 24, 'powers': [34, 31], 'representative': 228, 'size': 12}
  • id: 108500921
    {'aut_label': '24B1', 'centralizer': '12.e1.a1', 'counter': 45, 'group_counter': 155815, 'group_order': 1152, 'label': '24B-1', 'order': 24, 'powers': [34, 31], 'representative': 204, 'size': 12}
  • id: 108500922
    {'aut_label': '24C1', 'centralizer': '16.k1.a1', 'counter': 46, 'group_counter': 155815, 'group_order': 1152, 'label': '24C1', 'order': 24, 'powers': [36, 30], 'representative': 4, 'size': 16}
  • id: 108500923
    {'aut_label': '24C1', 'centralizer': '16.k1.a1', 'counter': 47, 'group_counter': 155815, 'group_order': 1152, 'label': '24C7', 'order': 24, 'powers': [36, 30], 'representative': 68, 'size': 16}
  • id: 108500924
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 48, 'group_counter': 155815, 'group_order': 1152, 'label': '24D1', 'order': 24, 'powers': [37, 30], 'representative': 388, 'size': 16}
  • id: 108500925
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 49, 'group_counter': 155815, 'group_order': 1152, 'label': '24D-1', 'order': 24, 'powers': [38, 30], 'representative': 196, 'size': 16}
  • id: 108500927
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 50, 'group_counter': 155815, 'group_order': 1152, 'label': '24D7', 'order': 24, 'powers': [38, 30], 'representative': 452, 'size': 16}
  • id: 108500928
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 51, 'group_counter': 155815, 'group_order': 1152, 'label': '24D-7', 'order': 24, 'powers': [37, 30], 'representative': 260, '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: 3897487
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897498
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897509
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897520
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897526
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897527
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897528
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897529
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897530
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 0, 0, -1, 2, -1, 2, 2, 0, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, -1, 0, 2, 2, 0, 0, -1, -1, 2, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3897488
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, -1, -1, 0, 0, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, 0, 0, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897489
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, -2, 0, 2, 2, 2, -2, -2, 0, 0, 0, 2, 2, 0, -2, 2, 2, 2, 2, 2, 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], 'schur_index': 1}
  • id: 3897490
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, -2, -2, 0, 0, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, 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], 'schur_index': 1}
  • id: 3897491
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, 0, -2, 2, -1, -1, 2, 2, -2, 0, 0, 0, 0, -2, 0, 2, 2, 2, -1, -1, 0, 0, 1, 2, 2, 0, 0, 2, 2, -1, -1, -1, 0, 0, 1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897492
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, 0, -2, 2, -1, -1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, -1, -1, 0, 0, 1, -2, -2, 0, 0, 2, 2, -1, -1, -1, 0, 0, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897493
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, -2, -2, 0, 0, -1, 2, -1, 2, 2, 0, -2, -2, 0, 0, 0, 0, -1, -1, -1, 2, -1, 1, 1, 0, 2, 2, 0, 0, -1, -1, 2, -1, -1, 1, 1, 0, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3897494
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, -2, 2, 0, 0, -1, 2, -1, 2, 2, 0, -2, 2, 0, 0, 0, 0, -1, -1, -1, 2, -1, 1, -1, 0, -2, -2, 0, 0, -1, -1, 2, -1, -1, 1, -1, 0, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3897495
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, -2, 0, 0, -1, 2, -1, 2, 2, 0, 2, -2, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, 1, 0, -2, -2, 0, 0, -1, -1, 2, -1, -1, -1, 1, 0, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3897496
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, 0, 2, 2, -1, -1, 2, 2, -2, 0, 0, 0, 0, -2, 0, 2, 2, 2, -1, -1, 0, 0, -1, -2, -2, 0, 0, 2, 2, -1, -1, -1, 0, 0, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897497
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 1, 1, 1, -1, 3, 0, 0, 3, -1, 3, -1, -1, 1, -1, -1, -1, 3, -1, -1, 0, 0, 1, 1, 0, 3, -1, -1, 1, 3, -1, 0, 0, 0, -1, -1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897499
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, -1, -1, -1, 3, 0, 0, 3, -1, 3, 1, 1, -1, 1, -1, 1, 3, -1, -1, 0, 0, -1, -1, 0, 3, -1, 1, -1, 3, -1, 0, 0, 0, 1, 1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897500
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, -1, 1, 1, 3, 0, 0, 3, -1, -3, 1, 1, 1, -1, 1, -1, 3, -1, -1, 0, 0, -1, -1, 0, 3, -1, -1, 1, 3, -1, 0, 0, 0, 1, 1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897501
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, 1, 1, 1, 3, 0, 0, 3, -1, 3, 1, -1, 1, -1, -1, -1, 3, -1, -1, 0, 0, -1, 1, 0, -3, 1, 1, -1, 3, -1, 0, 0, 0, 1, -1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897502
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, 1, -1, -1, 1, 3, 0, 0, 3, -1, 3, -1, 1, -1, 1, -1, 1, 3, -1, -1, 0, 0, 1, -1, 0, -3, 1, -1, 1, 3, -1, 0, 0, 0, -1, 1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897503
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, 1, 1, -1, 1, 3, 0, 0, 3, -1, -3, -1, -1, -1, 1, 1, 1, 3, -1, -1, 0, 0, 1, 1, 0, 3, -1, 1, -1, 3, -1, 0, 0, 0, -1, -1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897504
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, 1, -1, -1, 3, 0, 0, 3, -1, -3, 1, -1, -1, 1, 1, 1, 3, -1, -1, 0, 0, -1, 1, 0, -3, 1, -1, 1, 3, -1, 0, 0, 0, 1, -1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897505
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 1, -1, 1, -1, 3, 0, 0, 3, -1, -3, -1, 1, 1, -1, 1, -1, 3, -1, -1, 0, 0, 1, -1, 0, -3, 1, 1, -1, 3, -1, 0, 0, 0, -1, 1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897506
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 0, 0, 0, 4, 4, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3897507
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4b', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897508
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, -2, 4, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897510
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4d', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897511
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 0, 0, 0, -4, -4, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3897516
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6a', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 2, 2, 0, 0, -3, 0, 0, 6, -2, 0, -2, -2, 0, 0, 0, 0, -3, 1, 1, 0, 0, -1, -1, 0, 6, -2, 0, 0, -3, 1, 0, 0, 0, 1, 1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897517
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6b', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, -2, 0, 6, 0, 0, -6, 2, 0, 0, 0, 2, -2, 0, 2, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897518
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6c', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, 2, 0, 6, 0, 0, -6, 2, 0, 0, 0, -2, 2, 0, -2, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897519
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6d', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, -2, -2, 0, 0, -3, 0, 0, 6, -2, 0, 2, 2, 0, 0, 0, 0, -3, 1, 1, 0, 0, 1, 1, 0, 6, -2, 0, 0, -3, 1, 0, 0, 0, -1, -1, 0, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897521
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6e', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, -2, 2, 0, 0, -3, 0, 0, 6, -2, 0, 2, -2, 0, 0, 0, 0, -3, 1, 1, 0, 0, 1, -1, 0, -6, 2, 0, 0, -3, 1, 0, 0, 0, -1, 1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897522
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.6f', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 2, -2, 0, 0, -3, 0, 0, 6, -2, 0, -2, 2, 0, 0, 0, 0, -3, 1, 1, 0, 0, -1, 1, 0, -6, 2, 0, 0, -3, 1, 0, 0, 0, 1, -1, 0, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897512
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4f', 'multiplicity': 2, 'nt': [24, 140], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897513
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4g', 'multiplicity': 2, 'nt': [24, 141], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897514
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4h', 'multiplicity': 2, 'nt': [24, 231], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, -4, -4, 2, -8, -8, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897523
    {'cdim': 12, 'counter': 42, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.12a', 'multiplicity': 1, 'nt': [24, 935], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897524
    {'cdim': 12, 'counter': 43, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.12b', 'multiplicity': 1, 'nt': [36, 804], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 0, -6, 0, 0, -12, 4, 0, 0, 0, 0, 0, 0, 0, -6, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897515
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.4i', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, -8, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -8, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897525
    {'cdim': 12, 'counter': 44, 'faithful': True, 'group': '1152.155815', 'group_order': 1152, 'image': None, 'label': '1152.155815.12c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 8, -8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 5408579
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1152, 'label': '1152.155815.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408590
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 576, 'label': '1152.155815.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408601
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 576, 'label': '1152.155815.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408612
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 576, 'label': '1152.155815.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408623
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 576, 'label': '1152.155815.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408626
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 576, 'label': '1152.155815.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408627
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 576, 'label': '1152.155815.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408628
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 576, 'label': '1152.155815.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408629
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 192, 'label': '1152.155815.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408580
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 192, 'label': '1152.155815.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408581
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 288, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 144, 'label': '1152.155815.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408582
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 288, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 144, 'label': '1152.155815.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408583
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 96, 'label': '1152.155815.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408584
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 96, 'label': '1152.155815.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408585
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 96, 'label': '1152.155815.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408586
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 96, 'label': '1152.155815.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408587
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 96, 'label': '1152.155815.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408588
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 96, 'label': '1152.155815.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408589
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.a1', 'kernel_order': 48, 'label': '1152.155815.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408591
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.a1', 'kernel_order': 48, 'label': '1152.155815.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408592
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.155815.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408593
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.155815.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408594
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.155815.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408595
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.155815.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408596
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 24, 'label': '1152.155815.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408597
    {'center': '24.c1.a1', 'center_index': 24, 'center_order': 48, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 24, 'label': '1152.155815.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408598
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 32, 'label': '1152.155815.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408599
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 72, 'counter': 28, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 36, 'label': '1152.155815.4b', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408600
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 24, 'label': '1152.155815.4c', '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]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 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]]]}
  • id: 5408602
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 24, 'label': '1152.155815.4d', '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]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]]]}
  • id: 5408603
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 16, 'label': '1152.155815.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408604
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 24, 'counter': 32, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [-6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '96.121', 'image_order': 96, 'indicator': 1, 'kernel': '96.b1.a1', 'kernel_order': 12, 'label': '1152.155815.4f1', 'nt': [24, 140], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]]]}
  • id: 5408605
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 24, 'counter': 33, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [-6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '96.121', 'image_order': 96, 'indicator': 1, 'kernel': '96.b1.a1', 'kernel_order': 12, 'label': '1152.155815.4f2', 'nt': [24, 140], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]]]}
  • id: 5408606
    {'center': '48.b1.a1', 'center_index': 48, 'center_order': 24, 'counter': 34, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 12, 'label': '1152.155815.4g1', 'nt': [24, 141], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 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]], [[-4, 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]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
  • id: 5408607
    {'center': '48.b1.a1', 'center_index': 48, 'center_order': 24, 'counter': 35, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 12, 'label': '1152.155815.4g2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 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]], [[-4, 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]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
  • id: 5408608
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 36, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '144.145', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.155815.4h1', 'nt': [24, 231], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[3, 1]]]}
  • id: 5408609
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '144.145', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.155815.4h2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-3, 1]]]}
  • id: 5408610
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.446', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155815.4i1', '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]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 3], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 3], [2, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]]]}
  • id: 5408611
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 39, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.446', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155815.4i2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [2, 7]], [[1, 3], [-2, 7]]]}
  • id: 5408613
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 40, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.446', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155815.4i3', '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]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 3], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 3], [-2, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]]]}
  • id: 5408614
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 41, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.446', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155815.4i4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [1, 5]], [[1, 3], [-2, 7]], [[-1, 3], [2, 7]]]}
  • id: 5408615
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 42, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.155815.6a', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408616
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 43, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '192.1472', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 6, 'label': '1152.155815.6b', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 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: 5408617
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 44, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '192.1472', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 6, 'label': '1152.155815.6c', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 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: 5408618
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 45, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.155815.6d', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408619
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 46, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.155815.6e', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408620
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.155815.6f', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408621
    {'center': '192.a1.a1', 'center_index': 192, 'center_order': 6, 'counter': 48, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '384.18036', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 3, 'label': '1152.155815.12a', 'nt': [24, 935], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408622
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '576.8314', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 2, 'label': '1152.155815.12b', 'nt': [36, 804], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 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: 5408624
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 50, 'cyclotomic_n': 24, 'dim': 12, 'faithful': True, 'field': [6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.155815', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.155815.12c1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 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]], [[0, 0]], [[-3, 1], [3, 3], [-3, 5], [-6, 7]], [[3, 1], [-3, 3], [3, 5], [6, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408625
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 51, 'cyclotomic_n': 24, 'dim': 12, 'faithful': True, 'field': [6, 0, 1], 'group': '1152.155815', 'group_counter': 155815, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.155815', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.155815.12c2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 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]], [[0, 0]], [[3, 1], [-3, 3], [3, 5], [6, 7]], [[-3, 1], [3, 3], [-3, 5], [-6, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[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: 60973762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1152, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1152.155815.1.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': '1152.155815', 'subgroup_hash': 2811533159970853616, 'subgroup_order': 1152, 'subgroup_tex': 'C_{24}:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 60973873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8314', 'subgroup_hash': 8314, 'subgroup_order': 576, 'subgroup_tex': 'D_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': '576.5065', 'subgroup_hash': 5065, 'subgroup_order': 576, 'subgroup_tex': 'D_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '576.5570', 'subgroup_hash': 5570, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times C_{24}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 60974206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5470', 'subgroup_hash': 5470, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': '576.5069', 'subgroup_hash': 5069, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60974345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': '576.8302', 'subgroup_hash': 8302, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 60974356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 576, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.2.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': '576.5516', 'subgroup_hash': 5516, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '384.18036', 'subgroup_hash': 18036, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '384.13303', 'subgroup_hash': 13303, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 60973774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.920', 'subgroup_hash': 920, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60973785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.898', 'subgroup_hash': 898, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.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': '288.898', 'subgroup_hash': 898, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.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': '288.908', 'subgroup_hash': 908, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '288.918', 'subgroup_hash': 918, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60973829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 288, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '288.637', 'subgroup_hash': 637, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 60973840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.4.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': '288.402', 'subgroup_hash': 402, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.4.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': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.4.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': '288.855', 'subgroup_hash': 855, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 60973885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.853', 'subgroup_hash': 853, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 60973896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.4.l1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.446', 'subgroup_hash': 446, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1298', 'subgroup_hash': 1298, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60973918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 192, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.961', 'subgroup_hash': 961, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.1314', 'subgroup_hash': 1314, 'subgroup_order': 192, 'subgroup_tex': 'D_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.346', 'subgroup_hash': 346, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.448', 'subgroup_hash': 448, 'subgroup_order': 192, 'subgroup_tex': 'C_8:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 60973973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.713', 'subgroup_hash': 713, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.321', 'subgroup_hash': 321, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 60973996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.340', 'subgroup_hash': 340, 'subgroup_order': 192, 'subgroup_tex': 'D_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.445', 'subgroup_hash': 445, 'subgroup_order': 192, 'subgroup_tex': 'C_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.974', 'subgroup_hash': 974, 'subgroup_order': 192, 'subgroup_tex': 'D_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60974051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.1168', 'subgroup_hash': 1168, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '192.595', 'subgroup_hash': 595, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '192.899', 'subgroup_hash': 899, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.599', 'subgroup_hash': 599, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60974096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.1157', 'subgroup_hash': 1157, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 60974118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.1478', 'subgroup_hash': 1478, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.670', 'subgroup_hash': 670, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.959', 'subgroup_hash': 959, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.959', 'subgroup_hash': 959, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.8.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': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60974207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.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': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '144.56', 'subgroup_hash': 56, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '144.71', 'subgroup_hash': 71, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '144.72', 'subgroup_hash': 72, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times D_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60974284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.58', 'subgroup_hash': 58, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.139', 'subgroup_hash': 139, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.86', 'subgroup_hash': 86, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.8.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1152.155815.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1997', 'subgroup_hash': 1997, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 60974338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 96, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 96, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.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': '96.205', 'subgroup_hash': 205, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60974342
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 96, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.176', 'subgroup_hash': 176, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60974343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.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': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.138', 'subgroup_hash': 138, 'subgroup_order': 96, 'subgroup_tex': 'C_6:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.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': '96.179', 'subgroup_hash': 179, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60974357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60974359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.92', 'subgroup_hash': 92, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.210', 'subgroup_hash': 210, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.138', 'subgroup_hash': 138, 'subgroup_order': 96, 'subgroup_tex': 'C_6:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.143', 'subgroup_hash': 143, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.104', 'subgroup_hash': 104, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.107', 'subgroup_hash': 107, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 60974375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.57', 'subgroup_hash': 57, 'subgroup_order': 96, 'subgroup_tex': 'C_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.22', 'subgroup_hash': 22, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.21', 'subgroup_hash': 21, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60973767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.37', 'subgroup_hash': 37, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.199', 'subgroup_hash': 199, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.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': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60973783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.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': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.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': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60973786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.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': '96.121', 'subgroup_hash': 121, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.12.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 72, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.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': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.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': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.14', 'subgroup_hash': 14, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60973803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.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': '72.13', 'subgroup_hash': 13, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60973810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, '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: 60973812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.121', 'subgroup_hash': 121, 'subgroup_order': 64, 'subgroup_tex': '\\SD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, '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: 60973816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.149', 'subgroup_hash': 149, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 60973819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, '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: 60973820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, '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: 60973821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.147', 'subgroup_hash': 147, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 60973824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.116', 'subgroup_hash': 116, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 48, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.24.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': '24.14', '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60973843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60973859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60973860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60973880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ce1.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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cj1.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': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1.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': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1.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': '48.7', 'subgroup_hash': 7, 'subgroup_order': 48, 'subgroup_tex': 'D_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60973901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1.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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1.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': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1.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': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1.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': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1.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': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1.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': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1.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': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1.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': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1.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': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.de1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1.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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.df1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.24.dg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 36, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60973928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60973933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.32.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60973934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 32, 'counter': 254, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60973935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60973959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60973969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 60973980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, '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: 60973981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60973987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 301, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.48.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': '48.38', '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': ['S'], 'split': False, '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: 60973988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60973989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60973991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 24, 'counter': 305, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60973992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60973998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60973999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60974032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60974033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60974034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60974035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 348, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60974039
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974043
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60974046
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1.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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974047
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 356, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cd1.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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60974048
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1.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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ci1.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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cj1.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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1.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': 48, 'quotient_simple': 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: 60974058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1.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': 48, 'quotient_simple': 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: 60974060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.co1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cr1.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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1.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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ct1.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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1.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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cw1.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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.48.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx1.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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.64.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 16, 'counter': 386, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974115
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, '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: 60974141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cc1.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': 72, 'quotient_simple': None, '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: 60974142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cd1.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': 72, 'quotient_simple': None, '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: 60974143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ce1.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': 72, 'quotient_simple': None, '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: 60974144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cf1.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': 72, 'quotient_simple': None, '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: 60974145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cg1.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': 72, 'quotient_simple': None, '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: 60974146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ch1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60974147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ci1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60974148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cj1.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': 72, 'quotient_simple': None, '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: 60974149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ck1.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': 72, 'quotient_simple': None, '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: 60974150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cl1.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': 72, 'quotient_simple': None, '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: 60974152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.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': 72, 'quotient_simple': None, '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: 60974153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.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': 72, 'quotient_simple': None, '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: 60974154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cn1.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': 72, 'quotient_simple': None, '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: 60974155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.72.cn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cn1.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': 72, 'quotient_simple': None, '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: 60974156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 12, 'counter': 454, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.96.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974157
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 455, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.96.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': '96.121', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 121, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_6', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, '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: 60974158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 456, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.118', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 118, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974159
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974160
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974163
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974165
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974171
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 468, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974172
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974174
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974175
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974176
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974177
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974178
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974179
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60974180
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974187
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974188
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974196
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974197
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60974199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bn1.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': 96, 'quotient_simple': 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: 60974201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bo1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bo1.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': 96, 'quotient_simple': 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: 60974203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60974204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.96.bp1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bp1.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': 96, 'quotient_simple': 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: 60974205
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1152.155815.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 60974208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 500, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.145', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 145, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_6', '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: 60974209
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 8, 'counter': 501, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60974210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974211
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974225
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974247
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 536, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974248
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 537, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974252
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bv1.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': 144, 'quotient_simple': None, '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: 60974261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974263
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bw1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bw1.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': 144, 'quotient_simple': None, '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: 60974264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bx1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bx1.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': 144, 'quotient_simple': None, '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: 60974266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.by1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.by1.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': 144, 'quotient_simple': None, '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: 60974268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, '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: 60974271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.144.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cc1.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': 144, 'quotient_simple': None, '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: 60974272
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 6, 'counter': 559, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.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': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60974274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 560, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974275
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 561, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974276
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 562, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 60974277
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 563, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 60974278
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 60974279
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': 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: 60974280
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 566, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974281
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974282
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 568, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.192.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974283
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974285
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974286
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974287
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974288
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.192.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60974289
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 4, 'counter': 574, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60974290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 575, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155815.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.446', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 446, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2'], '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: 60974291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974293
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974296
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974298
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 582, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974299
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 583, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974300
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 584, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 585, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974307
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974308
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974309
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974310
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974311
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974319
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.288.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.bb1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bb1.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': 288, 'quotient_simple': 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: 60974322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60974323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155815.288.bc1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bc1.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': 288, 'quotient_simple': 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: 60974324
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 3, 'counter': 605, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '384.18036', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18036, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SD_{16}:S_4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 60974325
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.384.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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': 0}
  • id: 60974326
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.384.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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': 0}
  • id: 60974327
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 2, 'counter': 608, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155815.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8314', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8314, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_{12}:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], '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: 60974328
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974330
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974331
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974332
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974333
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974334
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974335
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155815.576.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60974336
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155815', 'ambient_counter': 155815, 'ambient_order': 1152, 'ambient_tex': 'C_{24}:(C_2\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 1, 'counter': 616, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1152.155815.1152.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1152.155815', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2811533159970853616, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{24}:(C_2\\times S_4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D3', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 60974287
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cx1.a1', '64.e1.a1', '96.m1.a1'], 'contains': ['384.c1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8879, -1, 1274, -1, 9272, -1, 637, -1], 'generators': [3, 416], 'label': '1152.155815.192.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.br1.a1', 'old_label': '192.n1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974304
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.z1.a1', '144.e1.a1'], 'contains': ['576.b1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5584, -1, 4694, -1, 5860, -1, 4348, -1], 'generators': [6, 720], 'label': '1152.155815.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1.a1', 'old_label': '288.o1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60973762
    {'ambient': '1152.155815', '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': '576.a1.a1', 'complements': ['1152.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', '3.b1.a1', '4.l1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6571, 5077, 4868, 5355, 7234, 5555, 3768, 5015], 'generators': [1, 576, 48, 32, 2, 24, 96, 384, 12], 'label': '1152.155815.1.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': '576.8314', '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': '576.8314'}
  • id: 60973763
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.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.n1.a1', '6.o1.a1', '6.p1.a1', '6.q1.a1', '6.s1.a1', '6.u1.a1', '9.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3433, -1, 6827, -1, 3618, -1, 7119, -1], 'generators': [1, 24, 96, 2, 576, 384, 48, 12], 'label': '1152.155815.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60973764
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '6.u1.a1'], 'contains': ['24.bd1.a1', '24.bf1.a1', '24.bh1.a1', '36.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1149, -1, 9483, -1, 2576, -1, 8401, -1], 'generators': [579, 384, 48, 588, 24, 96], 'label': '1152.155815.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bl1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973765
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.k1.a1'], 'contains': ['24.bn1.a1', '24.bq1.a1', '24.bu1.a1', '24.df1.a1', '24.df1.a2', '36.bh1.a1', '48.u1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9091, -1, 1010, -1, 9482, -1, 1180, -1], 'generators': [1, 576, 96, 2, 48, 32], 'label': '1152.155815.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.bm1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973766
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.k1.a1'], 'contains': ['24.bn1.a1', '24.bq1.a1', '24.bz1.a1', '36.bi1.a1', '48.v1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8534, -1, 1511, -1, 9062, -1, 2024, -1], 'generators': [73, 576, 96, 2, 48, 32], 'label': '1152.155815.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.bn1.a1', 'projective_image': '576.8314', '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': '96.226'}
  • id: 60973767
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.bn1.a1', '36.bj1.a1', '48.w1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5231, -1, 4953, -1, 8435, -1, 3130, -1], 'generators': [1, 576, 96, 72, 32, 48], 'label': '1152.155815.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bo1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60973768
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.n1.a1'], 'contains': ['24.d1.a1', '24.f1.a1', '24.j1.a1', '24.t1.a1', '24.bo1.a1', '24.bp1.a1', '24.bt1.a1', '24.de1.a1', '24.de1.a2', '24.dg1.a1', '24.dg1.a2', '36.bh1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7542, -1, 2178, -1, 8110, -1, 1713, -1], 'generators': [1, 384, 96, 2, 48, 576], 'label': '1152.155815.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.bp1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973769
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.n1.a1'], 'contains': ['24.e1.a1', '24.g1.a1', '24.k1.a1', '24.x1.a1', '24.bo1.a1', '24.bp1.a1', '24.bx1.a1', '36.bi1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6800, -1, 3453, -1, 7662, -1, 3322, -1], 'generators': [73, 384, 96, 2, 576, 48], 'label': '1152.155815.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.bq1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973770
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.n1.a1', '6.p1.a1', '6.q1.a1'], 'contains': ['24.a1.a1', '24.l1.a1', '24.m1.a1', '24.ba1.a1', '24.bp1.a1', '36.bk1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4723, -1, 5259, -1, 5535, -1, 4896, -1], 'generators': [2, 96, 48, 72, 576, 384], 'label': '1152.155815.12.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.br1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973771
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.s1.a1'], 'contains': ['24.n1.a1', '24.q1.a1', '24.w1.a1', '24.bk1.a1', '24.br1.a1', '24.bt1.a1', '24.bw1.a1', '36.bl1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6693, -1, 3519, -1, 5696, -1, 2931, -1], 'generators': [85, 384, 672, 6, 576, 48], 'label': '1152.155815.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.bs1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60973772
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.s1.a1'], 'contains': ['24.p1.a1', '24.r1.a1', '24.bl1.a1', '24.bm1.a1', '24.br1.a1', '24.bw1.a1', '24.bx1.a1', '36.bm1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6079, -1, 3764, -1, 5619, -1, 4452, -1], 'generators': [61, 384, 672, 6, 576, 48], 'label': '1152.155815.12.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.bt1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60973773
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.o1.a1', '6.p1.a1', '6.s1.a1'], 'contains': ['24.a1.a1', '24.o1.a1', '24.s1.a1', '24.bb1.a1', '24.br1.a1', '36.bn1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4648, -1, 5174, -1, 5239, -1, 4979, -1], 'generators': [6, 672, 48, 72, 576, 384], 'label': '1152.155815.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bu1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973774
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '12.a1.a1', '12.bo1.a1', '16.d1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5353, 5077, 4990, 6890, 7968, 5996, 3546, 7129], 'generators': [1, 576, 672, 72, 384, 32, 48], 'label': '1152.155815.4.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.b1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60973775
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.t1.a1'], 'contains': ['24.bs1.a1', '24.bu1.a1', '24.by1.a1', '36.bl1.a1', '48.bl1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8343, -1, 1725, -1, 8329, -1, 2067, -1], 'generators': [85, 576, 672, 6, 48, 32], 'label': '1152.155815.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.bv1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60973776
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.t1.a1'], 'contains': ['24.bs1.a1', '24.by1.a1', '24.bz1.a1', '36.bm1.a1', '48.bm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8233, -1, 1924, -1, 7931, -1, 2401, -1], 'generators': [61, 576, 672, 6, 48, 32], 'label': '1152.155815.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.bw1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973777
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.n1.a1', '6.s1.a1', '6.u1.a1'], 'contains': ['24.a1.a1', '24.u1.a1', '24.v1.a1', '24.bd1.a1', '24.bj1.a1', '24.bt1.a1', '24.bx1.a1', '36.bo1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5970, -1, 4359, -1, 5771, -1, 4564, -1], 'generators': [3, 384, 96, 72, 576, 48], 'label': '1152.155815.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bx1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60973778
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.k1.a1', '6.t1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '24.bu1.a1', '24.bz1.a1', '36.bo1.a1', '48.bq1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7640, -1, 2678, -1, 8192, -1, 2827, -1], 'generators': [3, 576, 96, 72, 48, 32], 'label': '1152.155815.12.by1.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.by1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60973779
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.w1.a1'], 'contains': ['24.bv1.a1', '24.ca1.a1', '24.cb1.a1', '36.bo1.a1', '48.br1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6139, -1, 5543, -1, 6806, -1, 3932, -1], 'generators': [3, 576, 96, 72, 48, 416], 'label': '1152.155815.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.bz1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973780
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.o1.a1', '6.q1.a1', '6.u1.a1'], 'contains': ['24.a1.a1', '24.bg1.a1', '24.bh1.a1', '36.bq1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4128, -1, 6232, -1, 4069, -1, 6955, -1], 'generators': [7, 384, 48, 576, 24, 672], 'label': '1152.155815.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ca1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60973781
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.m1.a1', '6.r1.a1', '6.t1.a1'], 'contains': ['24.b1.a1', '24.by1.a1', '36.bp1.a1', '48.ca1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7011, -1, 3575, -1, 7508, -1, 3070, -1], 'generators': [85, 576, 96, 72, 32, 48], 'label': '1152.155815.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.cb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60973782
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.l1.a1', '6.r1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '36.bq1.a1', '48.cc1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4907, -1, 5427, -1, 6554, -1, 5469, -1], 'generators': [7, 576, 672, 24, 48, 32], 'label': '1152.155815.12.cc1.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.cc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60973783
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.w1.a1'], 'contains': ['24.ca1.a1', '36.a1.a1', '48.cd1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4354, -1, 8222, -1, 5010, -1, 5903, -1], 'generators': [12, 576, 96, 416, 24, 48], 'label': '1152.155815.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '12.cd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60973784
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.w1.a1'], 'contains': ['24.ca1.a1', '36.bq1.a1', '48.ce1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4416, -1, 7709, -1, 4957, -1, 5970, -1], 'generators': [7, 576, 672, 24, 48, 416], 'label': '1152.155815.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.ce1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973785
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '12.b1.a1', '12.br1.a1', '16.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7044, 6291, 3596, 5648, 8046, 4859, 3268, 3743], 'generators': [2, 96, 32, 72, 576, 384, 48], 'label': '1152.155815.4.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.b1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60973786
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.l1.a1'], 'contains': ['24.cc1.a1', '24.cd1.a1', '24.ce1.a1', '24.cp1.a1', '24.cq1.a1', '24.cw1.a1', '24.cz1.a1', '36.br1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6572, -1, 4875, -1, 7332, -1, 3611, -1], 'generators': [1, 32, 48, 2, 12, 24], 'label': '1152.155815.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '12.cf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973787
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.c1.a1'], 'contains': ['24.c1.a1', '24.cg1.a1', '24.ch1.a1', '24.cj1.a1', '24.cm1.a1', '24.cr1.a1', '24.cx1.a1', '36.br1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3878, -1, 8280, -1, 1654, -1, 7878, -1], 'generators': [1, 384, 48, 2, 12, 24], 'label': '1152.155815.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.cg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973788
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.cg1.a1', '24.ch1.a1', '24.ci1.a1', '24.ck1.a1', '24.cn1.a1', '24.cs1.a1', '24.cy1.a1', '36.bs1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [564, -1, 9410, -1, 483, -1, 8843, -1], 'generators': [1, 384, 48, 2, 108, 24], 'label': '1152.155815.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.ch1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973789
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.ck1.a1', '24.cl1.a1', '24.cm1.a1', '24.cr1.a1', '24.cu1.a1', '24.cy1.a1', '24.db1.a1', '36.bt1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [400, -1, 9339, -1, 686, -1, 8802, -1], 'generators': [97, 384, 48, 2, 108, 24], 'label': '1152.155815.12.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.ci1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973790
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.cj1.a1', '24.cl1.a1', '24.cn1.a1', '24.cs1.a1', '24.cu1.a1', '24.cx1.a1', '24.dc1.a1', '36.bu1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [654, -1, 8976, -1, 852, -1, 8679, -1], 'generators': [97, 384, 48, 2, 12, 24], 'label': '1152.155815.12.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.cj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973791
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.t1.a1', '64.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8922, 7563, 1170, 2447, 9136, 6527, 1304, 2807], 'generators': [48, 576, 32, 384, 672], 'label': '1152.155815.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973792
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.e1.a1', '32.i1.a1', '32.i1.a2', '48.u1.a1', '48.x1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9300, -1, 870, -1, 9477, -1, 1369, -1], 'generators': [1, 384, 2, 48, 32], 'label': '1152.155815.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '16.b1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973793
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.h1.a1', '48.v1.a1', '48.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8831, -1, 1237, -1, 9400, -1, 1993, -1], 'generators': [73, 384, 2, 48, 32], 'label': '1152.155815.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '16.c1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973794
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '48.c1.a1', '48.w1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5351, -1, 4972, -1, 8507, -1, 3492, -1], 'generators': [1, 384, 72, 32, 48], 'label': '1152.155815.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.d1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973795
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.h1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.c1.a1', '32.f1.a1', '48.bc1.a1', '48.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7489, -1, 2899, -1, 8430, -1, 3217, -1], 'generators': [2, 32, 72, 384, 48], 'label': '1152.155815.16.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.e1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973796
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': ['288.bb1.a1', '288.bc1.a1', '288.bb1.a2', '288.bc1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '12.c1.a1', '12.bu1.a1', '16.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6821, 7512, 3671, 3132, 7687, 7133, 3341, 2625], 'generators': [6, 672, 32, 72, 576, 384, 48], 'label': '1152.155815.4.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.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60973797
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '8.m1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.g1.a1', '48.bf1.a1', '48.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8536, -1, 1769, -1, 8158, -1, 2305, -1], 'generators': [85, 384, 6, 48, 32], 'label': '1152.155815.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '16.f1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973798
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '8.m1.a1'], 'contains': ['32.d1.a1', '32.g1.a1', '32.h1.a1', '48.bh1.a1', '48.bm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8382, -1, 1963, -1, 8056, -1, 2441, -1], 'generators': [61, 384, 6, 48, 32], 'label': '1152.155815.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '16.g1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973799
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.i1.a1', '8.k1.a1', '8.m1.a1'], 'contains': ['32.d1.a1', '32.f1.a1', '48.bj1.a1', '48.bn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7224, -1, 3600, -1, 7809, -1, 3289, -1], 'generators': [6, 32, 72, 384, 48], 'label': '1152.155815.16.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.h1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973800
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.h1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.f1.a1', '32.h1.a1', '48.bo1.a1', '48.bq1.a1', '48.br1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7966, -1, 2758, -1, 7977, -1, 3144, -1], 'generators': [3, 384, 72, 48, 32], 'label': '1152.155815.16.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.i1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973801
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.j1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.f1.a1', '32.g1.a1', '48.d1.a1', '48.ca1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7289, -1, 3822, -1, 7502, -1, 3402, -1], 'generators': [85, 384, 72, 32, 48], 'label': '1152.155815.16.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.j1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973802
    {'ambient': '1152.155815', 'aut_centralizer_order': 72, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.j1.a1', '8.k1.a1', '8.n1.a1'], 'contains': ['32.f1.a1', '48.e1.a1', '48.cb1.a1', '48.cd1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5032, -1, 5649, -1, 6256, -1, 5343, -1], 'generators': [12, 48, 32, 384, 24], 'label': '1152.155815.16.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60973803
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.i1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.f1.a1', '48.bw1.a1', '48.cc1.a1', '48.ce1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5147, -1, 5495, -1, 6113, -1, 5404, -1], 'generators': [7, 384, 24, 48, 32], 'label': '1152.155815.16.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.l1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973804
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.o1.a1', '8.o1.a2'], 'contains': ['32.a1.a1', '48.cp1.a1', '48.cq1.a1', '64.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9738, -1, 377, -1, 9845, -1, 205, -1], 'generators': [1, 384, 32, 672, 576], 'label': '1152.155815.16.m1.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': '16.m1.a1', 'projective_image': '1152.155815', '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': '144.183'}
  • id: 60973805
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.o1.a1', '8.o1.a2'], 'contains': ['32.a1.a1', '48.cr1.a1', '48.cs1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9794, -1, 90, -1, 9908, -1, 322, -1], 'generators': [2, 576, 384, 32, 96], 'label': '1152.155815.16.n1.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': '16.n1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973806
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.a1.a1', '48.ct1.a1', '48.cu1.a1', '64.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9201, -1, 557, -1, 9282, -1, 902, -1], 'generators': [6, 576, 384, 32, 672], 'label': '1152.155815.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.o1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973807
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '288.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.bx1.a1', '12.by1.a1', '12.bz1.a1', '16.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7225, 9012, 3410, 557, 7810, 9490, 3178, 889], 'generators': [3, 96, 384, 72, 576, 48, 32], 'label': '1152.155815.4.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', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60973808
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.a1', '8.o1.a2'], 'contains': ['32.a1.a1', '48.cv1.a1', '48.cw1.a1', '48.cx1.a1', '64.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9582, -1, 286, -1, 9791, -1, 272, -1], 'generators': [3, 576, 32, 384, 96], 'label': '1152.155815.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.p1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60973809
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.f1.a1', '36.j1.a1', '36.l1.a1', '36.q1.a1', '36.w1.a1', '36.br1.a1', '36.bs1.a1', '36.bt1.a1', '36.bu1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1766, -1, 8372, -1, 2246, -1, 8740, -1], 'generators': [1, 2, 12, 96], 'label': '1152.155815.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973810
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.h1.a1', '36.i1.a1', '36.m1.a1', '36.n1.a1', '36.v1.a1', '36.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3110, -1, 6778, -1, 3573, -1, 7355, -1], 'generators': [1, 2, 588], 'label': '1152.155815.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973811
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.g1.a1', '36.i1.a1', '36.s1.a1', '36.t1.a1', '36.be1.a1', '36.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1989, -1, 8515, -1, 3321, -1, 8239, -1], 'generators': [1, 578, 588], 'label': '1152.155815.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973812
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '36.h1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.bf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3649, -1, 6218, -1, 3855, -1, 7076, -1], 'generators': [1, 578, 12], 'label': '1152.155815.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973813
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.j1.a1', '36.k1.a1', '36.n1.a1', '36.r1.a1', '36.t1.a1', '36.ba1.a1', '36.bf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2843, -1, 7700, -1, 3237, -1, 8050, -1], 'generators': [577, 2, 12], 'label': '1152.155815.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973814
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.k1.a1', '36.l1.a1', '36.m1.a1', '36.y1.a1', '36.z1.a1', '36.bc1.a1', '36.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1585, -1, 7515, -1, 3412, -1, 7205, -1], 'generators': [577, 2, 588], 'label': '1152.155815.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973815
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.q1.a1', '36.r1.a1', '36.s1.a1', '36.u1.a1', '36.x1.a1', '36.y1.a1', '36.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2677, -1, 7861, -1, 2940, -1, 7826, -1], 'generators': [577, 578, 588], 'label': '1152.155815.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973816
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.a1.a1'], 'contains': ['36.u1.a1', '36.v1.a1', '36.w1.a1', '36.z1.a1', '36.ba1.a1', '36.bd1.a1', '36.be1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2315, -1, 6879, -1, 3484, -1, 7272, -1], 'generators': [577, 578, 12], 'label': '1152.155815.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.h1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973817
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.n1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '36.g1.a1', '36.k1.a1', '36.u1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1', '36.bk1.a1', '36.bo1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5225, -1, 4694, -1, 5831, -1, 4836, -1], 'generators': [1, 2, 72, 576], 'label': '1152.155815.18.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973818
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': ['288.bb1.a1', '288.bc1.a1', '288.bb1.a2', '288.bc1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '12.d1.a1', '12.cb1.a1', '16.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6950, 2570, 4161, 4390, 7409, 3708, 3473, 8240], 'generators': [85, 576, 672, 72, 384, 32, 48], 'label': '1152.155815.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60973819
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.o1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.h1.a1', '36.r1.a1', '36.z1.a1', '36.bj1.a1', '36.bn1.a1', '36.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3949, -1, 5992, -1, 4478, -1, 6817, -1], 'generators': [1, 6, 576], 'label': '1152.155815.18.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.j1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973820
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.m1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.f1.a1', '36.i1.a1', '36.y1.a1', '36.ba1.a1', '36.bj1.a1', '36.bp1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3751, -1, 6419, -1, 4255, -1, 9063, -1], 'generators': [1, 12, 96, 576], 'label': '1152.155815.18.k1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973821
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.j1.a1', '36.m1.a1', '36.s1.a1', '36.bd1.a1', '36.bk1.a1', '36.bn1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4110, -1, 5823, -1, 4631, -1, 6605, -1], 'generators': [2, 12, 576], 'label': '1152.155815.18.l1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973822
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.r1.a1', '9.a1.a1'], 'contains': ['36.l1.a1', '36.n1.a1', '36.bb1.a1', '36.be1.a1', '36.bk1.a1', '36.bp1.a1', '36.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4035, -1, 5909, -1, 4375, -1, 7569, -1], 'generators': [85, 2, 576], 'label': '1152.155815.18.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.m1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973823
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '6.t1.a1', '9.a1.a1'], 'contains': ['36.o1.a1', '36.p1.a1', '36.q1.a1', '36.t1.a1', '36.v1.a1', '36.bc1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1', '36.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5088, -1, 4812, -1, 4899, -1, 5355, -1], 'generators': [85, 6, 72, 576], 'label': '1152.155815.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973824
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.v1.a1', '6.w1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.w1.a1', '36.x1.a1', '36.bf1.a1', '36.bg1.a1', '36.bo1.a1', '36.bq1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3834, -1, 9625, -1, 4562, -1, 7937, -1], 'generators': [3, 12, 576], 'label': '1152.155815.18.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.o1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973825
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1', '12.br1.a1', '12.bu1.a1', '12.bx1.a1', '12.ca1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.l1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4581, 3923, 5334, 5633, 5491, 3749, 5553, 6092], 'generators': [72, 48, 96, 576, 384], 'label': '1152.155815.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60973826
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.c1.a1', '12.f1.a1', '12.bo1.a1', '12.by1.a1', '12.cb1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '96.s1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7027, 5798, 3149, 3930, 8359, 5306, 2876, 3830], 'generators': [72, 576, 32, 48, 96], 'label': '1152.155815.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1', '12.c1.a1', '12.f1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973827
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '48.b1.a1', 'complements': ['48.cs1.a1', '48.cu1.a1', '48.cw1.a1', '48.cx1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.k1.a1', '12.cg1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '72.bu1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4256, 1717, 6771, 8766, 1469, 1123, 8045, 7910], 'generators': [1, 384, 12, 24, 48], 'label': '1152.155815.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973828
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.bp1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.i1.a1', '48.x1.a1', '48.ba1.a1', '48.cf1.a1', '48.cl1.a1', '48.cl1.a2', '72.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6595, -1, 3583, -1, 6978, -1, 2529, -1], 'generators': [1, 384, 2, 48, 96], 'label': '1152.155815.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.d1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973829
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '48.e1.a1', 'complements': ['288.bb1.a1', '288.bc1.a1', '288.bb1.a2', '288.bc1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.e1.a1', '12.f1.a1', '12.cd1.a1', '16.k1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4796, 1357, 5777, 8403, 6547, 1937, 5445, 4847], 'generators': [12, 672, 48, 32, 576, 384, 24], 'label': '1152.155815.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '576.8314', '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: 60973830
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.i1.a1', '12.bq1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.r1.a1', '48.y1.a1', '48.bb1.a1', '72.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6246, -1, 3957, -1, 6334, -1, 4167, -1], 'generators': [73, 384, 2, 96, 48], 'label': '1152.155815.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.e1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973831
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.l1.a1', '12.bp1.a1'], 'contains': ['48.f1.a1', '48.n1.a1', '48.q1.a1', '48.cm1.a1', '48.cm1.a2', '72.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6668, -1, 3408, -1, 7412, -1, 1926, -1], 'generators': [1, 384, 578, 48, 96], 'label': '1152.155815.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.f1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973832
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.l1.a1', '12.bq1.a1'], 'contains': ['48.f1.a1', '48.n1.a1', '48.s1.a1', '72.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6727, -1, 3630, -1, 7264, -1, 2678, -1], 'generators': [73, 384, 578, 48, 96], 'label': '1152.155815.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.g1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973833
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.f1.a1', '48.j1.a1', '48.l1.a1', '48.z1.a1', '48.bt1.a1', '72.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6166, -1, 4020, -1, 6179, -1, 4824, -1], 'generators': [1, 384, 648, 96, 48], 'label': '1152.155815.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.h1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973834
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.k1.a1', '48.z1.a1', '48.bs1.a1', '72.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3247, -1, 6664, -1, 2612, -1, 6828, -1], 'generators': [1, 384, 72, 96, 48], 'label': '1152.155815.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973835
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.p1.a1', '12.bp1.a1'], 'contains': ['48.g1.a1', '48.j1.a1', '48.q1.a1', '48.cn1.a1', '48.cn1.a2', '72.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6466, -1, 3680, -1, 7202, -1, 2183, -1], 'generators': [577, 384, 2, 48, 96], 'label': '1152.155815.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.j1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973836
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.p1.a1', '12.bq1.a1'], 'contains': ['48.g1.a1', '48.j1.a1', '48.s1.a1', '48.cg1.a1', '72.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6532, -1, 3743, -1, 6901, -1, 3744, -1], 'generators': [649, 384, 2, 96, 144], 'label': '1152.155815.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.k1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973837
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.br1.a1'], 'contains': ['48.g1.a1', '48.l1.a1', '48.n1.a1', '72.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6382, -1, 3860, -1, 6735, -1, 3957, -1], 'generators': [2, 96, 648, 384, 144], 'label': '1152.155815.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.l1.a1', 'projective_image': '576.8314', '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': '16.14'}
  • id: 60973838
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1', '12.br1.a1'], 'contains': ['48.g1.a1', '48.k1.a1', '48.bc1.a1', '48.bd1.a1', '72.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2696, -1, 7256, -1, 2096, -1, 6478, -1], 'generators': [2, 48, 72, 96, 384], 'label': '1152.155815.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60973839
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.v1.a1', '12.bs1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.m1.a1', '48.bf1.a1', '48.bg1.a1', '72.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5463, -1, 4774, -1, 4783, -1, 5271, -1], 'generators': [85, 384, 6, 672, 48], 'label': '1152.155815.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.n1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973840
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '288.a1.a1', 'complements': ['288.bb1.a1', '288.bc1.a1', '288.bb1.a2', '288.bc1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.ca1.a1', '12.cc1.a1', '12.ce1.a1', '16.l1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5032, 3828, 5577, 1845, 6467, 8311, 5520, 5984], 'generators': [7, 672, 384, 24, 576, 48, 32], 'label': '1152.155815.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60973841
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.u1.a1', '12.bu1.a1'], 'contains': ['48.h1.a1', '48.l1.a1', '48.o1.a1', '72.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5547, -1, 4635, -1, 5403, -1, 4706, -1], 'generators': [6, 672, 648, 384, 720], 'label': '1152.155815.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.o1.a1', 'projective_image': '576.8314', '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': '16.14'}
  • id: 60973842
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '12.v1.a1', '12.bt1.a1'], 'contains': ['48.h1.a1', '48.m1.a1', '48.r1.a1', '48.bh1.a1', '48.bi1.a1', '72.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5150, -1, 5027, -1, 4620, -1, 5471, -1], 'generators': [61, 384, 6, 672, 48], 'label': '1152.155815.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.p1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973843
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '12.y1.a1', '12.bs1.a1'], 'contains': ['48.h1.a1', '48.p1.a1', '48.q1.a1', '72.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5382, -1, 4540, -1, 5171, -1, 4768, -1], 'generators': [661, 384, 6, 48, 672], 'label': '1152.155815.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.q1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973844
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.y1.a1', '12.bt1.a1'], 'contains': ['48.h1.a1', '48.p1.a1', '48.s1.a1', '72.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5653, -1, 4381, -1, 5073, -1, 4644, -1], 'generators': [637, 384, 6, 48, 672], 'label': '1152.155815.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.r1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973845
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.o1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1', '12.bu1.a1'], 'contains': ['48.h1.a1', '48.k1.a1', '48.bj1.a1', '48.bk1.a1', '72.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1231, -1, 8748, -1, 1181, -1, 7159, -1], 'generators': [6, 48, 72, 672, 384], 'label': '1152.155815.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.s1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60973846
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.z1.a1', '12.bp1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '48.n1.a1', '48.co1.a1', '48.co1.a2', '72.r1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6777, -1, 3479, -1, 7324, -1, 2109, -1], 'generators': [577, 384, 578, 48, 96], 'label': '1152.155815.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.t1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973847
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.v1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1', '12.bc1.a1', '12.bx1.a1'], 'contains': ['48.i1.a1', '48.k1.a1', '48.r1.a1', '48.bo1.a1', '48.bp1.a1', '72.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1315, -1, 7337, -1, 3014, -1, 6281, -1], 'generators': [3, 384, 72, 96, 48], 'label': '1152.155815.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.u1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973848
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.t1.a1', '12.bx1.a1'], 'contains': ['48.i1.a1', '48.l1.a1', '48.s1.a1', '72.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6070, -1, 4097, -1, 6064, -1, 4110, -1], 'generators': [3, 384, 648, 48, 96], 'label': '1152.155815.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.v1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973849
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.ba1.a1', '12.bs1.a1'], 'contains': ['48.i1.a1', '48.o1.a1', '48.p1.a1', '72.u1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5823, -1, 4269, -1, 5294, -1, 2809, -1], 'generators': [661, 384, 582, 48, 672], 'label': '1152.155815.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.w1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973850
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.z1.a1', '12.bq1.a1'], 'contains': ['48.j1.a1', '48.n1.a1', '48.r1.a1', '72.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6311, -1, 3793, -1, 6668, -1, 4019, -1], 'generators': [649, 384, 578, 144, 96], 'label': '1152.155815.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.x1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973851
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.o1.a1', '8.o1.a2', '12.bm1.a1', '12.bp1.a1', '16.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8938, -1, 993, -1, 9177, -1, 1357, -1], 'generators': [1, 96, 384, 2, 576, 48, 32], 'label': '1152.155815.4.h1.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.h1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60973852
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.p1.a1', '12.w1.a1', '12.z1.a1', '12.bd1.a1', '12.be1.a1', '12.bf1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.bs1.a1', '48.bt1.a1', '72.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1711, -1, 7617, -1, 1607, -1, 6756, -1], 'generators': [577, 384, 72, 96, 48], 'label': '1152.155815.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.y1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973853
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.k1.a1', '12.q1.a1', '12.v1.a1', '12.bd1.a1', '12.bg1.a1', '12.bh1.a1'], 'contains': ['48.d1.a1', '48.k1.a1', '48.m1.a1', '48.bu1.a1', '48.bx1.a1', '72.x1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3033, -1, 7762, -1, 1408, -1, 7340, -1], 'generators': [85, 384, 72, 96, 48], 'label': '1152.155815.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.z1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973854
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.x1.a1', '12.z1.a1', '12.bg1.a1', '12.bi1.a1', '12.bj1.a1', '12.br1.a1'], 'contains': ['48.k1.a1', '48.n1.a1', '72.y1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3312, -1, 6301, -1, 3360, -1, 5959, -1], 'generators': [578, 96, 72, 384, 48], 'label': '1152.155815.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.ba1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60973855
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.r1.a1', '12.ba1.a1', '12.be1.a1', '12.bh1.a1', '12.bi1.a1', '12.bu1.a1'], 'contains': ['48.k1.a1', '48.o1.a1', '72.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3408, -1, 6137, -1, 3624, -1, 5885, -1], 'generators': [582, 672, 72, 384, 48], 'label': '1152.155815.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bb1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60973856
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.n1.a1', '12.s1.a1', '12.y1.a1', '12.ba1.a1', '12.bf1.a1', '12.bj1.a1'], 'contains': ['48.k1.a1', '48.p1.a1', '48.bu1.a1', '48.by1.a1', '72.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2356, -1, 7423, -1, 2455, -1, 7414, -1], 'generators': [661, 384, 72, 96, 48], 'label': '1152.155815.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bc1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60973857
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.p1.a1', '12.y1.a1', '12.bh1.a1', '12.bk1.a1', '12.bl1.a1', '12.bx1.a1'], 'contains': ['48.k1.a1', '48.q1.a1', '48.s1.a1', '72.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2231, -1, 8005, -1, 4036, -1, 5050, -1], 'generators': [579, 384, 72, 48, 96], 'label': '1152.155815.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bd1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973858
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.k1.a1', '12.o1.a1', '12.bb1.a1', '12.bf1.a1', '12.bi1.a1', '12.bk1.a1'], 'contains': ['48.e1.a1', '48.k1.a1', '48.bv1.a1', '72.bc1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1588, -1, 8125, -1, 1330, -1, 9035, -1], 'generators': [12, 48, 96, 384, 24], 'label': '1152.155815.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '576.8314', '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: 60973859
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.n1.a1', '12.r1.a1', '12.x1.a1', '12.bc1.a1', '12.bd1.a1', '12.bl1.a1'], 'contains': ['48.k1.a1', '48.bv1.a1', '72.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1024, -1, 9094, -1, 1529, -1, 8963, -1], 'generators': [588, 48, 96, 384, 24], 'label': '1152.155815.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bf1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60973860
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.s1.a1', '12.w1.a1', '12.bc1.a1', '12.bg1.a1', '12.bk1.a1', '12.ca1.a1'], 'contains': ['48.k1.a1', '48.bz1.a1', '72.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2423, -1, 7117, -1, 1685, -1, 7616, -1], 'generators': [583, 384, 672, 696, 48], 'label': '1152.155815.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bg1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973861
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.q1.a1', '12.bb1.a1', '12.be1.a1', '12.bj1.a1', '12.bl1.a1', '12.ca1.a1'], 'contains': ['48.k1.a1', '48.bw1.a1', '72.bf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [800, -1, 8922, -1, 1252, -1, 8577, -1], 'generators': [7, 384, 672, 24, 48], 'label': '1152.155815.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bh1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973862
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '12.bn1.a1', '12.bq1.a1', '16.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8626, -1, 1508, -1, 9029, -1, 2024, -1], 'generators': [73, 96, 384, 2, 576, 48, 32], 'label': '1152.155815.4.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': '576.8314', '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': '288.1028'}
  • id: 60973863
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.t1.a1', '12.u1.a1'], 'contains': ['48.l1.a1', '48.m1.a1', '48.p1.a1', '48.bx1.a1', '48.by1.a1', '72.bg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5021, -1, 4945, -1, 4704, -1, 5812, -1], 'generators': [85, 384, 648, 96, 48], 'label': '1152.155815.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.bi1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973864
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.u1.a1', '12.bx1.a1'], 'contains': ['48.l1.a1', '48.q1.a1', '48.r1.a1', '72.bh1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5934, -1, 4175, -1, 6021, -1, 4368, -1], 'generators': [579, 384, 648, 48, 96], 'label': '1152.155815.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bj1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973865
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '12.bh1.a1', '12.bs1.a1'], 'contains': ['48.m1.a1', '48.o1.a1', '48.q1.a1', '72.bi1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5602, -1, 4435, -1, 5337, -1, 2718, -1], 'generators': [85, 384, 582, 48, 672], 'label': '1152.155815.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.bk1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973866
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.bh1.a1', '12.bt1.a1'], 'contains': ['48.m1.a1', '48.o1.a1', '48.s1.a1', '72.bj1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5771, -1, 4318, -1, 5232, -1, 4425, -1], 'generators': [61, 384, 582, 48, 672], 'label': '1152.155815.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.bl1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973867
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '12.ba1.a1', '12.bt1.a1'], 'contains': ['48.o1.a1', '48.p1.a1', '48.r1.a1', '72.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5340, -1, 4693, -1, 5023, -1, 4887, -1], 'generators': [637, 384, 582, 48, 672], 'label': '1152.155815.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.bm1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973868
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.b1.a1', '48.cp1.a1', '72.bl1.a1', '96.e1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9182, -1, 950, -1, 9550, -1, 1180, -1], 'generators': [1, 576, 48, 32, 96], 'label': '1152.155815.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bn1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973869
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.j1.a1', '48.ch1.a1', '48.cq1.a1', '72.bl1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7871, -1, 2164, -1, 8583, -1, 1812, -1], 'generators': [1, 384, 48, 96, 576], 'label': '1152.155815.24.bo1.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.bo1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973870
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bp1.a1', '12.bq1.a1', '12.br1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.n1.a1', '48.ci1.a1', '48.cr1.a1', '72.bm1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7989, -1, 2093, -1, 8653, -1, 1747, -1], 'generators': [2, 96, 48, 576, 384], 'label': '1152.155815.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bp1.a1', 'projective_image': '576.8314', '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': '16.14'}
  • id: 60973871
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.a1', '12.bm1.a1', '12.bn1.a1'], 'contains': ['48.b1.a1', '48.cs1.a1', '72.bm1.a1', '96.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 1020, -1, 9619, -1, 1099, -1], 'generators': [2, 576, 48, 32, 96], 'label': '1152.155815.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bq1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973872
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bs1.a1', '12.bt1.a1', '12.bu1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.o1.a1', '48.cj1.a1', '48.ct1.a1', '72.bn1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7394, -1, 2575, -1, 6406, -1, 2250, -1], 'generators': [6, 672, 48, 576, 384], 'label': '1152.155815.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '24.br1.a1', 'projective_image': '576.8314', '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': '16.14'}
  • id: 60973873
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.i1.a1', '6.k1.a1', '6.n1.a1', '8.h1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7235, 7483, 3394, 5355, 8046, 6913, 3157, 3851], 'generators': [1, 32, 384, 2, 48, 576, 96, 72], 'label': '1152.155815.2.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': '576.8314', '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': '576.8314'}
  • id: 60973874
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '12.bs1.a1', '12.bv1.a1', '16.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8421, -1, 1725, -1, 8117, -1, 2290, -1], 'generators': [85, 672, 384, 6, 576, 48, 32], 'label': '1152.155815.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.j1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60973875
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.c1.a1', '12.bv1.a1', '12.bw1.a1'], 'contains': ['48.b1.a1', '48.cu1.a1', '72.bn1.a1', '96.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8472, -1, 1655, -1, 8953, -1, 1467, -1], 'generators': [6, 576, 48, 32, 672], 'label': '1152.155815.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '24.bs1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973876
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bp1.a1', '12.bs1.a1', '12.bx1.a1'], 'contains': ['48.a1.a1', '48.i1.a1', '48.q1.a1', '48.ck1.a1', '48.cv1.a1', '72.bo1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7808, -1, 2226, -1, 8288, -1, 1680, -1], 'generators': [3, 384, 48, 576, 96], 'label': '1152.155815.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bt1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973877
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '144.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bm1.a1', '12.bv1.a1', '12.by1.a1'], 'contains': ['48.b1.a1', '48.cw1.a1', '72.bo1.a1', '96.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8982, -1, 1101, -1, 9218, -1, 1245, -1], 'generators': [3, 576, 48, 32, 96], 'label': '1152.155815.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bu1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973878
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bz1.a1'], 'contains': ['48.t1.a1', '48.cx1.a1', '72.bo1.a1', '96.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8043, -1, 2297, -1, 8871, -1, 1526, -1], 'generators': [3, 576, 48, 416, 96], 'label': '1152.155815.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.bv1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973879
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.d1.a1', '12.bs1.a1', '12.bt1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '48.p1.a1', '72.bp1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7259, -1, 2893, -1, 5772, -1, 4306, -1], 'generators': [85, 384, 96, 576, 48], 'label': '1152.155815.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '24.bw1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973880
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.bq1.a1', '12.bt1.a1', '12.bx1.a1'], 'contains': ['48.a1.a1', '48.r1.a1', '48.s1.a1', '72.bq1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7441, -1, 2725, -1, 6460, -1, 3802, -1], 'generators': [75, 384, 576, 48, 96], 'label': '1152.155815.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bx1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60973881
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.bv1.a1', '12.bw1.a1', '12.cb1.a1'], 'contains': ['48.b1.a1', '72.bp1.a1', '96.t1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8323, -1, 1765, -1, 8216, -1, 2043, -1], 'generators': [85, 576, 32, 48, 96], 'label': '1152.155815.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.by1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973882
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '144.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.bn1.a1', '12.bw1.a1', '12.by1.a1'], 'contains': ['48.b1.a1', '72.bq1.a1', '96.u1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8645, -1, 1567, -1, 8800, -1, 2384, -1], 'generators': [75, 576, 48, 32, 96], 'label': '1152.155815.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bz1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973883
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bz1.a1', '12.cd1.a1', '12.ce1.a1'], 'contains': ['48.t1.a1', '72.a1.a1', '96.v1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4719, -1, 7190, -1, 5967, -1, 4234, -1], 'generators': [72, 576, 416, 48, 96], 'label': '1152.155815.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '24.ca1.a1', 'projective_image': '576.8314', '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': '24.12'}
  • id: 60973884
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.bz1.a1'], 'contains': ['48.t1.a1', '72.bq1.a1', '96.w1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7743, -1, 2760, -1, 7581, -1, 3010, -1], 'generators': [75, 576, 48, 416, 96], 'label': '1152.155815.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.cb1.a1', 'projective_image': '576.8314', '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': '48.48'}
  • id: 60973885
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.g1.a1', '12.bt1.a1', '12.bw1.a1', '16.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8263, -1, 2230, -1, 7890, -1, 2440, -1], 'generators': [61, 672, 384, 6, 576, 48, 32], 'label': '1152.155815.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60973886
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.h1.a1', '12.cf1.a1'], 'contains': ['48.u1.a1', '48.v1.a1', '48.w1.a1', '48.be1.a1', '48.bq1.a1', '72.bs1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8111, -1, 2363, -1, 9036, -1, 2627, -1], 'generators': [1, 32, 2, 72, 48], 'label': '1152.155815.24.cc1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973887
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '8.i1.a1', '12.cf1.a1'], 'contains': ['48.w1.a1', '48.bn1.a1', '48.cc1.a1', '72.bt1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5696, -1, 5080, -1, 7624, -1, 3687, -1], 'generators': [1, 32, 6, 72, 48], 'label': '1152.155815.24.cd1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973888
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '8.j1.a1', '12.cf1.a1'], 'contains': ['48.w1.a1', '48.ca1.a1', '48.cb1.a1', '72.bu1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5258, -1, 5456, -1, 7110, -1, 3577, -1], 'generators': [1, 48, 12, 32, 24], 'label': '1152.155815.24.ce1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.ce1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973889
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1'], 'contains': ['48.x1.a1', '48.y1.a1', '48.z1.a1', '48.ba1.a1', '48.bb1.a1', '48.bd1.a1', '48.bp1.a1', '72.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2854, -1, 6474, -1, 3244, -1, 5203, -1], 'generators': [1, 384, 2, 168, 48], 'label': '1152.155815.24.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '24.cf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973890
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.i1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.x1.a1', '48.y1.a1', '48.bc1.a1', '48.bo1.a1', '72.bs1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3751, -1, 6607, -1, 2383, -1, 6539, -1], 'generators': [1, 384, 2, 72, 48], 'label': '1152.155815.24.cg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973891
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.j1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.bj1.a1', '48.bw1.a1', '72.bt1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [886, -1, 9601, -1, 569, -1, 8273, -1], 'generators': [1, 384, 6, 72, 48], 'label': '1152.155815.24.ch1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.ch1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973892
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.n1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.bu1.a1', '48.bv1.a1', '72.bv1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1969, -1, 8341, -1, 483, -1, 9944, -1], 'generators': [1, 384, 108, 24, 48], 'label': '1152.155815.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.ci1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973893
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.o1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bc1.a1', '48.bj1.a1', '72.bw1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2482, -1, 8399, -1, 976, -1, 8095, -1], 'generators': [2, 48, 12, 384, 72], 'label': '1152.155815.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973894
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.ch1.a1', '12.ci1.a1'], 'contains': ['48.bc1.a1', '48.bj1.a1', '48.bv1.a1', '72.bx1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [291, -1, 9682, -1, 159, -1, 9270, -1], 'generators': [2, 48, 108, 384, 72], 'label': '1152.155815.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.ck1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973895
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.bc1.a1', '48.bo1.a1', '48.bs1.a1', '72.by1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [583, -1, 9209, -1, 911, -1, 6935, -1], 'generators': [97, 384, 2, 72, 48], 'label': '1152.155815.24.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cl1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973896
    {'ambient': '1152.155815', 'aut_centralizer_order': 1, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.153175', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '12.cf1.a1', '12.cg1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6606, -1, 4901, -1, 7014, -1, 3841, -1], 'generators': [1, 32, 48, 2, 384, 12, 24], 'label': '1152.155815.4.l1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '4.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.145'}
  • id: 60973897
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.q1.a1', '12.cg1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bc1.a1', '48.bw1.a1', '72.bz1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [396, -1, 8821, -1, 686, -1, 8214, -1], 'generators': [85, 384, 2, 72, 48], 'label': '1152.155815.24.cm1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cm1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973898
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.bc1.a1', '48.bu1.a1', '48.bw1.a1', '72.ca1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [230, -1, 9520, -1, 289, -1, 9151, -1], 'generators': [181, 384, 2, 72, 48], 'label': '1152.155815.24.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cn1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973899
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1'], 'contains': ['48.bd1.a1', '48.by1.a1', '48.bz1.a1', '72.cb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2618, -1, 6895, -1, 1106, -1, 7490, -1], 'generators': [661, 384, 2, 168, 48], 'label': '1152.155815.24.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.co1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60973900
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.k1.a1', '12.cf1.a1'], 'contains': ['48.be1.a1', '48.bn1.a1', '48.cb1.a1', '72.bw1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6872, -1, 3279, -1, 7667, -1, 3346, -1], 'generators': [2, 32, 12, 72, 48], 'label': '1152.155815.24.cp1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '24.cp1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973901
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '8.l1.a1', '12.cf1.a1'], 'contains': ['48.be1.a1', '48.ca1.a1', '48.cc1.a1', '72.bz1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6907, -1, 4853, -1, 7036, -1, 3646, -1], 'generators': [85, 32, 2, 72, 48], 'label': '1152.155815.24.cq1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cq1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973902
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.v1.a1', '12.cg1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bf1.a1', '48.bh1.a1', '48.bj1.a1', '48.bo1.a1', '72.cc1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1843, -1, 8872, -1, 803, -1, 6986, -1], 'generators': [85, 384, 6, 72, 48], 'label': '1152.155815.24.cr1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cr1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973903
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.bg1.a1', '48.bi1.a1', '48.bj1.a1', '48.bo1.a1', '48.bu1.a1', '72.cd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [449, -1, 9441, -1, 17, -1, 8004, -1], 'generators': [757, 384, 6, 72, 48], 'label': '1152.155815.24.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cs1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60974042
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '24.bi1.a1', '24.co1.a1'], 'contains': ['96.o1.a1', '96.q1.a1', '144.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2651, -1, 6941, -1, 2619, -1, 7011, -1], 'generators': [661, 168, 48, 384], 'label': '1152.155815.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '48.by1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60973904
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1'], 'contains': ['48.bf1.a1', '48.bg1.a1', '48.bh1.a1', '48.bi1.a1', '48.bk1.a1', '48.bp1.a1', '48.bx1.a1', '72.ce1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1155, -1, 9354, -1, 104, -1, 6700, -1], 'generators': [85, 384, 6, 744, 48], 'label': '1152.155815.24.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '24.ct1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973905
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.bj1.a1', '48.bs1.a1', '48.bw1.a1', '72.cf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [336, -1, 9798, -1, 61, -1, 9091, -1], 'generators': [673, 384, 6, 72, 48], 'label': '1152.155815.24.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cu1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973906
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1'], 'contains': ['48.bk1.a1', '48.bt1.a1', '48.bz1.a1', '72.cg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1807, -1, 8501, -1, 439, -1, 7108, -1], 'generators': [97, 384, 6, 744, 48], 'label': '1152.155815.24.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1.a1', 'old_label': '24.cv1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60973907
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '144.a1.a1', 'complements': ['192.i1.a1', '192.k1.a1', '192.m1.a1', '192.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.k1.a1', '12.n1.a1', '12.bd1.a1', '12.bf1.a1', '18.k1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3537, 621, 7163, 9248, 3618, 731, 8760, 9431], 'generators': [1, 48, 24, 12, 384, 96, 576], 'label': '1152.155815.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60973908
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '8.m1.a1', '12.cf1.a1'], 'contains': ['48.bl1.a1', '48.bm1.a1', '48.bn1.a1', '48.bq1.a1', '48.ca1.a1', '72.cc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7925, -1, 2450, -1, 7893, -1, 2931, -1], 'generators': [85, 32, 6, 72, 48], 'label': '1152.155815.24.cw1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cw1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973909
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.bb1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bo1.a1', '48.bw1.a1', '72.ch1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2041, -1, 8976, -1, 1036, -1, 8681, -1], 'generators': [3, 384, 12, 24, 48], 'label': '1152.155815.24.cx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cx1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973910
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '12.ch1.a1', '12.ci1.a1'], 'contains': ['48.bo1.a1', '48.bv1.a1', '48.bw1.a1', '72.ci1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [171, -1, 9986, -1, 219, -1, 9376, -1], 'generators': [3, 384, 108, 24, 48], 'label': '1152.155815.24.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cy1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973911
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '8.n1.a1', '12.cf1.a1'], 'contains': ['48.bq1.a1', '48.cb1.a1', '48.cc1.a1', '72.ch1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4934, -1, 5605, -1, 6547, -1, 5147, -1], 'generators': [3, 32, 12, 24, 48], 'label': '1152.155815.24.cz1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cz1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973912
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '8.n1.a1'], 'contains': ['48.br1.a1', '48.cd1.a1', '48.ce1.a1', '72.ch1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4463, -1, 8237, -1, 4529, -1, 6141, -1], 'generators': [3, 416, 12, 24, 48], 'label': '1152.155815.24.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1.a1', 'old_label': '24.da1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60973913
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bd1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bs1.a1', '48.bv1.a1', '72.cj1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [850, -1, 9016, -1, 353, -1, 9423, -1], 'generators': [97, 384, 108, 24, 48], 'label': '1152.155815.24.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.db1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973914
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bf1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bs1.a1', '48.bu1.a1', '72.ck1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1403, -1, 7898, -1, 526, -1, 9463, -1], 'generators': [97, 384, 12, 24, 48], 'label': '1152.155815.24.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.dc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973915
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bd1.a1', '12.bf1.a1'], 'contains': ['48.bs1.a1', '48.bu1.a1', '48.bv1.a1', '72.cl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1090, -1, 8307, -1, 396, -1, 9984, -1], 'generators': [577, 384, 108, 24, 48], 'label': '1152.155815.24.dd1.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.dd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60973916
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1'], 'contains': ['48.ch1.a1', '48.ci1.a1', '48.ck1.a1', '48.cl1.a1', '48.cm1.a1', '48.cn1.a1', '48.co1.a1', '72.cm1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8195, -1, 1998, -1, 9346, -1, 1022, -1], 'generators': [1, 384, 2, 624, 96], 'label': '1152.155815.24.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.de1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973917
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1'], 'contains': ['48.ch1.a1', '48.ci1.a1', '48.ck1.a1', '48.cl1.a2', '48.cm1.a2', '48.cn1.a2', '48.co1.a2', '72.cm1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8195, -1, 1946, -1, 9346, -1, 962, -1], 'generators': [577, 384, 2, 624, 96], 'label': '1152.155815.24.de1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.de1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973918
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': ['192.g1.a1', '192.o1.a1', '192.l1.a1', '192.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.f1.a1', '18.l1.a1', '24.cp1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6631, 6843, 3863, 5798, 7571, 2812, 3415, 1757], 'generators': [2, 96, 32, 12, 576, 72, 48], 'label': '1152.155815.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60973919
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.bm1.a1'], 'contains': ['48.cp1.a1', '48.cs1.a1', '48.cw1.a1', '72.cn1.a1', '96.bn1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9591, -1, 409, -1, 9972, -1, 81, -1], 'generators': [1, 576, 2, 32, 96], 'label': '1152.155815.24.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '24.df1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60973920
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a2', '12.bm1.a1'], 'contains': ['48.cp1.a1', '48.cs1.a1', '48.cw1.a1', '72.cn1.a2', '96.bn1.a2'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9591, -1, 343, -1, 9972, -1, 141, -1], 'generators': [49, 576, 2, 32, 96], 'label': '1152.155815.24.df1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '24.df1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60973921
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.bp1.a1'], 'contains': ['48.cl1.a1', '48.cm1.a2', '48.cn1.a2', '48.co1.a1', '48.cq1.a1', '48.cr1.a1', '48.cv1.a1', '72.cn1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8883, -1, 1225, -1, 9720, -1, 640, -1], 'generators': [1, 384, 2, 576, 96], 'label': '1152.155815.24.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.dg1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973922
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a2', '12.bp1.a1'], 'contains': ['48.cl1.a2', '48.cm1.a1', '48.cn1.a1', '48.co1.a2', '48.cq1.a1', '48.cr1.a1', '48.cv1.a1', '72.cn1.a2'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8883, -1, 1153, -1, 9720, -1, 716, -1], 'generators': [49, 384, 2, 576, 96], 'label': '1152.155815.24.dg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.dg1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60973923
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': ['36.br1.a1', '36.bu1.a1', '36.bs1.a1', '36.bt1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.m1.a1', '16.n1.a1', '16.o1.a1', '16.p1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.bm1.a1', '128.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9747, 7637, 108, 2335, 9787, 6527, 200, 2524], 'generators': [32, 384, 672, 576], 'label': '1152.155815.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['96.b1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '1152.155815', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60973924
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '96.e1.a1', '96.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9403, -1, 665, -1, 9314, -1, 1730, -1], 'generators': [1, 48, 32, 384], 'label': '1152.155815.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.b1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973925
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1'], 'contains': ['64.a1.a1', '64.c1.a1', '96.g1.a1', '96.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9349, -1, 731, -1, 9250, -1, 1670, -1], 'generators': [2, 48, 384, 32], 'label': '1152.155815.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.c1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973926
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '96.i1.a1', '96.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8774, -1, 1429, -1, 8022, -1, 2302, -1], 'generators': [6, 48, 384, 32], 'label': '1152.155815.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '32.d1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973927
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1', '16.f1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '96.k1.a1', '96.l1.a1', '96.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9276, -1, 952, -1, 8530, -1, 2178, -1], 'generators': [3, 48, 32, 384], 'label': '1152.155815.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.e1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973928
    {'ambient': '1152.155815', 'aut_centralizer_order': 144, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.d1.a1', '16.e1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.s1.a1', '96.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7200, -1, 3095, -1, 7564, -1, 4139, -1], 'generators': [72, 32, 384, 48], 'label': '1152.155815.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.f1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60973929
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.i1.a1', '12.j1.a1', '12.k1.a1', '12.o1.a1', '12.q1.a1', '12.v1.a1', '12.bb1.a1', '12.cg1.a1', '12.ch1.a1', '12.ci1.a1', '12.cj1.a1', '18.a1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1858, -1, 8485, -1, 1515, -1, 8542, -1], 'generators': [1, 48, 24, 2, 384, 12, 96], 'label': '1152.155815.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.c1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973930
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '16.f1.a1', '16.g1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '96.p1.a1', '96.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8596, -1, 1645, -1, 7705, -1, 2891, -1], 'generators': [85, 32, 48, 384], 'label': '1152.155815.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '32.g1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973931
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '16.c1.a1', '16.g1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '96.r1.a1', '96.u1.a1', '96.w1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8540, -1, 1491, -1, 8288, -1, 3066, -1], 'generators': [75, 48, 32, 384], 'label': '1152.155815.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.h1.a1', 'projective_image': '576.8314', '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': '72.46'}
  • id: 60973932
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '16.b1.a1'], 'contains': ['64.b1.a1', '64.c1.a1', '64.e1.a1', '96.bn1.a1', '96.bo1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9862, -1, 434, -1, 9873, -1, 248, -1], 'generators': [1, 2, 32, 384], 'label': '1152.155815.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.i1.a1', 'projective_image': '1152.155815', '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': '36.10'}
  • id: 60973933
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a2', '16.b1.a1'], 'contains': ['64.b1.a1', '64.c1.a1', '64.e1.a1', '96.bn1.a2', '96.bo1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9862, -1, 201, -1, 9873, -1, 301, -1], 'generators': [49, 2, 32, 384], 'label': '1152.155815.32.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.i1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60973934
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.e1.a1', 'complements': ['32.i1.a1', '32.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '12.cd1.a1', '18.k1.a1', '18.l1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.bc1.a1', '72.bd1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3995, 3923, 6430, 6657, 4381, 2571, 8329, 4941], 'generators': [12, 96, 576], 'label': '1152.155815.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.e1.a1', '12.f1.a1'], 'normal_contains': ['72.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60973935
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '72.f1.a1', '72.i1.a1', '72.j1.a1', '72.r1.a1', '72.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6458, -1, 3753, -1, 6820, -1, 3860, -1], 'generators': [1, 2, 648], 'label': '1152.155815.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973936
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.i1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.f1.a1', '72.h1.a1', '72.j1.a1', '72.v1.a1', '72.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6372, -1, 3822, -1, 6620, -1, 4065, -1], 'generators': [577, 2, 648], 'label': '1152.155815.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973937
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.a1.a1', '18.b1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.g1.a1', '72.k1.a1', '72.s1.a1', '72.br1.a1', '72.bs1.a1', '72.by1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3210, -1, 6691, -1, 3828, -1, 6413, -1], 'generators': [1, 2, 72, 96], 'label': '1152.155815.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973938
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.a1.a1', '18.c1.a1', '18.j1.a1'], 'contains': ['72.g1.a1', '72.q1.a1', '72.bf1.a1', '72.bt1.a1', '72.cf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1220, -1, 9074, -1, 1757, -1, 8798, -1], 'generators': [1, 6, 672], 'label': '1152.155815.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973939
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.a1.a1', '18.d1.a1', '18.k1.a1'], 'contains': ['72.g1.a1', '72.x1.a1', '72.bc1.a1', '72.bu1.a1', '72.bv1.a1', '72.cj1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3386, -1, 6560, -1, 2011, -1, 9679, -1], 'generators': [1, 12, 96], 'label': '1152.155815.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973940
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.i1.a1', '12.m1.a1', '12.n1.a1', '12.r1.a1', '12.s1.a1', '12.ba1.a1', '12.bc1.a1', '18.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2769, -1, 6827, -1, 3075, -1, 7119, -1], 'generators': [1, 48, 96, 2, 384, 588, 24], 'label': '1152.155815.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973941
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.c1.a1', '18.d1.a1', '18.i1.a1'], 'contains': ['72.d1.a1', '72.e1.a1', '72.g1.a1', '72.y1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3766, -1, 5942, -1, 4450, -1, 5745, -1], 'generators': [1, 578, 72], 'label': '1152.155815.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973942
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.b1.a1', '18.d1.a1', '18.j1.a1'], 'contains': ['72.g1.a1', '72.z1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3596, -1, 6088, -1, 3931, -1, 7026, -1], 'generators': [1, 582], 'label': '1152.155815.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973943
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.b1.a1', '18.c1.a1', '18.k1.a1'], 'contains': ['72.g1.a1', '72.ba1.a1', '72.bd1.a1', '72.bv1.a1', '72.cl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2639, -1, 7520, -1, 2912, -1, 9875, -1], 'generators': [1, 588, 96], 'label': '1152.155815.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973944
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.a1.a1', '18.e1.a1', '18.l1.a1'], 'contains': ['72.k1.a1', '72.q1.a1', '72.bc1.a1', '72.bw1.a1', '72.bx1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1745, -1, 8712, -1, 1822, -1, 8738, -1], 'generators': [2, 12, 96], 'label': '1152.155815.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973945
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.e1.a1', '18.f1.a1', '18.i1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.k1.a1', '72.w1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2272, -1, 7461, -1, 4097, -1, 6016, -1], 'generators': [577, 2, 72], 'label': '1152.155815.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973946
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.a1.a1', '18.f1.a1', '18.m1.a1'], 'contains': ['72.k1.a1', '72.x1.a1', '72.bf1.a1', '72.bz1.a1', '72.ca1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [888, -1, 8645, -1, 1906, -1, 8491, -1], 'generators': [85, 2, 96], 'label': '1152.155815.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973947
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.b1.a1', '18.f1.a1', '18.l1.a1'], 'contains': ['72.k1.a1', '72.z1.a1', '72.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3132, -1, 7039, -1, 3769, -1, 7067, -1], 'generators': [2, 588], 'label': '1152.155815.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973948
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '18.b1.a1', '18.e1.a1', '18.m1.a1'], 'contains': ['72.k1.a1', '72.ba1.a1', '72.be1.a1', '72.cb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2951, -1, 6850, -1, 3160, -1, 7803, -1], 'generators': [661, 2, 96], 'label': '1152.155815.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973949
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '18.n1.a1'], 'contains': ['72.l1.a1', '72.m1.a1', '72.p1.a1', '72.t1.a1', '72.u1.a1', '72.bg1.a1', '72.bj1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5604, -1, 4579, -1, 4973, -1, 4603, -1], 'generators': [85, 6, 648], 'label': '1152.155815.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '36.o1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973950
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '18.n1.a1'], 'contains': ['72.m1.a1', '72.n1.a1', '72.o1.a1', '72.bg1.a1', '72.bh1.a1', '72.bi1.a1', '72.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5264, -1, 4647, -1, 4924, -1, 4938, -1], 'generators': [661, 6, 648], 'label': '1152.155815.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '36.p1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973951
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.j1.a1', '12.l1.a1', '12.n1.a1', '12.x1.a1', '12.y1.a1', '12.bj1.a1', '12.bl1.a1', '18.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1947, -1, 7908, -1, 2796, -1, 7716, -1], 'generators': [1, 48, 96, 578, 384, 588, 24], 'label': '1152.155815.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973952
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.a1.a1', '18.g1.a1', '18.n1.a1'], 'contains': ['72.l1.a1', '72.n1.a1', '72.q1.a1', '72.s1.a1', '72.x1.a1', '72.cc1.a1', '72.cd1.a1', '72.ce1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1655, -1, 8556, -1, 2534, -1, 7226, -1], 'generators': [85, 6, 72, 672], 'label': '1152.155815.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.q1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973953
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.e1.a1', '18.g1.a1', '18.j1.a1'], 'contains': ['72.q1.a1', '72.w1.a1', '72.be1.a1', '72.cg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2569, -1, 7762, -1, 2318, -1, 7724, -1], 'generators': [577, 6, 672], 'label': '1152.155815.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973954
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.c1.a1', '18.g1.a1', '18.l1.a1'], 'contains': ['72.q1.a1', '72.y1.a1', '72.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2101, -1, 8771, -1, 3086, -1, 7913, -1], 'generators': [578, 588], 'label': '1152.155815.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.s1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973955
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.c1.a1', '18.e1.a1', '18.n1.a1'], 'contains': ['72.o1.a1', '72.p1.a1', '72.q1.a1', '72.ba1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1945, -1, 8276, -1, 3974, -1, 6659, -1], 'generators': [661, 6, 72], 'label': '1152.155815.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973956
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1'], 'contains': ['72.r1.a1', '72.s1.a1', '72.v1.a1', '72.w1.a1', '72.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2765, -1, 6957, -1, 4146, -1, 6210, -1], 'generators': [577, 578, 72], 'label': '1152.155815.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.u1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973957
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.b1.a1', '18.h1.a1', '18.n1.a1'], 'contains': ['72.s1.a1', '72.u1.a1', '72.z1.a1', '72.ba1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3076, -1, 6757, -1, 4199, -1, 6353, -1], 'generators': [661, 582, 72], 'label': '1152.155815.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.v1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973958
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.a1.a1', '18.h1.a1', '18.o1.a1'], 'contains': ['72.s1.a1', '72.bc1.a1', '72.bf1.a1', '72.ch1.a1', '72.ci1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1579, -1, 9973, -1, 2703, -1, 8878, -1], 'generators': [3, 12, 96], 'label': '1152.155815.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.w1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973959
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.b1.a1', '18.g1.a1', '18.o1.a1'], 'contains': ['72.s1.a1', '72.bd1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2885, -1, 9137, -1, 3513, -1, 7958, -1], 'generators': [3, 588], 'label': '1152.155815.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.x1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973960
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.f1.a1', '18.g1.a1', '18.k1.a1'], 'contains': ['72.w1.a1', '72.x1.a1', '72.bd1.a1', '72.cj1.a1', '72.cl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1447, -1, 7931, -1, 2180, -1, 9582, -1], 'generators': [577, 588, 96], 'label': '1152.155815.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.y1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973961
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.f1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.w1.a1', '72.z1.a1', '72.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1325, -1, 7103, -1, 3465, -1, 7283, -1], 'generators': [577, 582], 'label': '1152.155815.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.z1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973962
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.k1.a1', '12.l1.a1', '12.m1.a1', '12.bg1.a1', '12.bh1.a1', '12.bi1.a1', '12.bk1.a1', '18.d1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3433, -1, 6529, -1, 3184, -1, 6864, -1], 'generators': [1, 48, 96, 578, 384, 12, 24], 'label': '1152.155815.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973963
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.e1.a1', '18.h1.a1', '18.k1.a1'], 'contains': ['72.w1.a1', '72.ba1.a1', '72.bc1.a1', '72.ck1.a1', '72.cl1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2498, -1, 7293, -1, 2808, -1, 9777, -1], 'generators': [577, 12, 96], 'label': '1152.155815.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ba1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973964
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.d1.a1', '18.g1.a1', '18.m1.a1'], 'contains': ['72.x1.a1', '72.y1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3706, -1, 6239, -1, 3562, -1, 7673, -1], 'generators': [85, 578], 'label': '1152.155815.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973965
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.d1.a1', '18.f1.a1', '18.n1.a1'], 'contains': ['72.x1.a1', '72.z1.a1', '72.bb1.a1', '72.bi1.a1', '72.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3872, -1, 5994, -1, 4258, -1, 6067, -1], 'generators': [85, 582, 72], 'label': '1152.155815.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973966
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.d1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.y1.a1', '72.z1.a1', '72.bc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3812, -1, 6052, -1, 3887, -1, 6885, -1], 'generators': [578, 12], 'label': '1152.155815.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973967
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.c1.a1', '18.h1.a1', '18.m1.a1'], 'contains': ['72.y1.a1', '72.ba1.a1', '72.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1805, -1, 7396, -1, 3298, -1, 7872, -1], 'generators': [661, 578], 'label': '1152.155815.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.be1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973968
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.d1.a1', '18.e1.a1', '18.o1.a1'], 'contains': ['72.bb1.a1', '72.bc1.a1', '72.be1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3292, -1, 8152, -1, 3705, -1, 8403, -1], 'generators': [579, 12], 'label': '1152.155815.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973969
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '18.c1.a1', '18.f1.a1', '18.o1.a1'], 'contains': ['72.bb1.a1', '72.bd1.a1', '72.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1175, -1, 9913, -1, 3421, -1, 8634, -1], 'generators': [579, 588], 'label': '1152.155815.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973970
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '12.bp1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.h1.a1', '72.r1.a1', '72.bl1.a1', '72.bm1.a1', '72.bo1.a1', '72.cm1.a1', '72.cm1.a2', '72.cn1.a1', '72.cn1.a2'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8008, -1, 2169, -1, 8722, -1, 1591, -1], 'generators': [1, 2, 48, 576], 'label': '1152.155815.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.bh1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60973971
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.bq1.a1', '18.i1.a1'], 'contains': ['72.c1.a1', '72.e1.a1', '72.i1.a1', '72.v1.a1', '72.bl1.a1', '72.bm1.a1', '72.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7507, -1, 2651, -1, 7729, -1, 3069, -1], 'generators': [73, 2, 576], 'label': '1152.155815.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.bi1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973972
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bo1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.g1.a1', '72.w1.a1', '72.bl1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4431, -1, 5597, -1, 5572, -1, 5679, -1], 'generators': [1, 72, 96, 576], 'label': '1152.155815.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973973
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.o1.a1', '12.p1.a1', '12.s1.a1', '12.w1.a1', '12.y1.a1', '12.bf1.a1', '12.bk1.a1', '18.e1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2456, -1, 7541, -1, 2708, -1, 7455, -1], 'generators': [577, 48, 96, 2, 384, 12, 24], 'label': '1152.155815.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973974
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.br1.a1', '18.i1.a1', '18.l1.a1', '18.m1.a1'], 'contains': ['72.a1.a1', '72.j1.a1', '72.k1.a1', '72.y1.a1', '72.bm1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4681, -1, 5210, -1, 5636, -1, 4988, -1], 'generators': [2, 72, 576], 'label': '1152.155815.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bk1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973975
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.bv1.a1', '18.n1.a1'], 'contains': ['72.l1.a1', '72.o1.a1', '72.u1.a1', '72.bi1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7361, -1, 2706, -1, 5844, -1, 2764, -1], 'generators': [85, 6, 576], 'label': '1152.155815.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '36.bl1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973976
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '12.bw1.a1', '18.n1.a1'], 'contains': ['72.n1.a1', '72.p1.a1', '72.bj1.a1', '72.bk1.a1', '72.bn1.a1', '72.bp1.a1', '72.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7058, -1, 3042, -1, 5696, -1, 4492, -1], 'generators': [61, 6, 576], 'label': '1152.155815.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '36.bm1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60973977
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.bu1.a1', '18.j1.a1', '18.l1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.m1.a1', '72.q1.a1', '72.z1.a1', '72.bn1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4846, -1, 5152, -1, 5122, -1, 5619, -1], 'generators': [6, 72, 576], 'label': '1152.155815.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bn1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60973978
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '12.by1.a1', '12.bz1.a1', '18.i1.a1', '18.n1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.s1.a1', '72.t1.a1', '72.bb1.a1', '72.bh1.a1', '72.bo1.a1', '72.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6067, -1, 4391, -1, 5903, -1, 4553, -1], 'generators': [3, 72, 576], 'label': '1152.155815.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bo1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973979
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.cb1.a1', '18.k1.a1', '18.m1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.x1.a1', '72.ba1.a1', '72.bg1.a1', '72.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4613, -1, 5306, -1, 4860, -1, 6604, -1], 'generators': [85, 72, 96, 576], 'label': '1152.155815.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bp1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973980
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '12.cc1.a1', '12.ce1.a1', '18.j1.a1', '18.m1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.be1.a1', '72.bf1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4049, -1, 5880, -1, 4317, -1, 7554, -1], 'generators': [7, 576], 'label': '1152.155815.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bq1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60973981
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '12.cg1.a1', '18.a1.a1'], 'contains': ['72.bs1.a1', '72.bt1.a1', '72.bu1.a1', '72.bw1.a1', '72.bz1.a1', '72.cc1.a1', '72.ch1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4348, -1, 6350, -1, 2259, -1, 8150, -1], 'generators': [1, 2, 12], 'label': '1152.155815.36.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.br1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973982
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '18.a1.a1'], 'contains': ['72.bs1.a1', '72.bt1.a1', '72.bv1.a1', '72.bx1.a1', '72.ca1.a1', '72.cd1.a1', '72.ci1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [449, -1, 9671, -1, 618, -1, 9508, -1], 'generators': [1, 2, 108], 'label': '1152.155815.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bs1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973983
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '18.a1.a1'], 'contains': ['72.bx1.a1', '72.by1.a1', '72.bz1.a1', '72.cc1.a1', '72.cf1.a1', '72.ci1.a1', '72.cj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [91, -1, 9628, -1, 755, -1, 9325, -1], 'generators': [97, 2, 108], 'label': '1152.155815.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bt1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973984
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.e1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1', '6.l1.a1', '6.o1.a1', '8.i1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5353, 5077, 4990, 6559, 7268, 8015, 3929, 5931], 'generators': [1, 32, 384, 6, 48, 576, 672, 72], 'label': '1152.155815.2.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.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60973985
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.p1.a1', '12.q1.a1', '12.r1.a1', '12.bd1.a1', '12.be1.a1', '12.bh1.a1', '12.bl1.a1', '18.f1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1693, -1, 7654, -1, 2883, -1, 6955, -1], 'generators': [577, 48, 96, 2, 384, 588, 24], 'label': '1152.155815.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973986
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.a1.a1'], 'contains': ['72.bw1.a1', '72.by1.a1', '72.ca1.a1', '72.cd1.a1', '72.cf1.a1', '72.ch1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [494, -1, 9397, -1, 852, -1, 9215, -1], 'generators': [97, 2, 12], 'label': '1152.155815.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bu1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60973987
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.bo1.a1', '24.bp1.a1', '24.br1.a1', '24.bt1.a1', '24.bw1.a1', '24.bx1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.bd1.a1', '144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7698, 5644, 2426, 4322, 7782, 4590, 2029, 4416], 'generators': [48, 96, 576, 384], 'label': '1152.155815.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1', '144.a1.a1', '192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60973988
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '24.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.bn1.a1', '24.bq1.a1', '24.bs1.a1', '24.bu1.a1', '24.by1.a1', '24.bz1.a1'], 'contains': ['96.c1.a1', '144.a1.a1', '192.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9111, 6718, 1035, 3222, 8602, 5596, 1525, 3433], 'generators': [48, 32, 96, 576], 'label': '1152.155815.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1'], 'normal_contains': ['96.c1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60973989
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.c1.a1', '24.i1.a1', '24.cg1.a1', '24.ch1.a1', '24.ci1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '144.t1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3885, 2732, 6638, 8035, 2750, 2130, 7112, 7412], 'generators': [1, 72, 48, 384], 'label': '1152.155815.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.a1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973990
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '48.b1.a1', 'complements': ['24.df1.a1', '24.df1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.c1.a1', '24.z1.a1', '24.cm1.a1', '24.cr1.a1', '24.db1.a1'], 'contains': ['96.a1.a1', '96.p1.a1', '144.bi1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1853, 2063, 8297, 7350, 1810, 1502, 7447, 8024], 'generators': [85, 72, 48, 384], 'label': '1152.155815.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['12.d1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60973991
    {'ambient': '1152.155815', 'aut_centralizer_order': 576, 'aut_label': '48.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.f1.a1', 'complements': ['24.df1.a1', '24.df1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.c1.a1', '24.be1.a1', '24.cj1.a1', '24.cx1.a1', '24.dc1.a1'], 'contains': ['96.a1.a1', '144.b1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2311, 1401, 7966, 8758, 2372, 882, 8142, 6813], 'generators': [12, 384, 24, 48], 'label': '1152.155815.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['12.e1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60973992
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.bo1.a1'], 'contains': ['96.d1.a1', '96.f1.a1', '96.n1.a1', '96.x1.a1', '96.be1.a1', '144.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6653, -1, 3540, -1, 6734, -1, 3264, -1], 'generators': [1, 48, 96, 384], 'label': '1152.155815.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.f1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60973993
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.bp1.a1'], 'contains': ['96.d1.a1', '96.g1.a1', '96.y1.a1', '96.bf1.a1', '144.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6576, -1, 3688, -1, 6808, -1, 3949, -1], 'generators': [2, 48, 96, 384], 'label': '1152.155815.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.g1.a1', 'projective_image': '576.8314', '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': '8.5'}
  • id: 60973994
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.br1.a1'], 'contains': ['96.d1.a1', '96.i1.a1', '96.z1.a1', '96.bg1.a1', '144.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5121, -1, 4911, -1, 5073, -1, 4992, -1], 'generators': [6, 48, 672, 384], 'label': '1152.155815.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '48.h1.a1', 'projective_image': '576.8314', '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': '8.5'}
  • id: 60973995
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.n1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1', '24.bt1.a1'], 'contains': ['96.d1.a1', '96.k1.a1', '96.ba1.a1', '96.bh1.a1', '144.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6033, -1, 4039, -1, 6067, -1, 3126, -1], 'generators': [3, 48, 96, 384], 'label': '1152.155815.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.i1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973996
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.v1.a1', '12.w1.a1', '12.x1.a1', '12.z1.a1', '12.bc1.a1', '12.bd1.a1', '12.bg1.a1', '18.g1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2314, -1, 7843, -1, 2617, -1, 7291, -1], 'generators': [577, 48, 96, 578, 384, 588, 24], 'label': '1152.155815.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60973997
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.j1.a1', '24.k1.a1', '24.t1.a1', '24.x1.a1', '24.y1.a1', '24.bo1.a1'], 'contains': ['96.d1.a1', '96.n1.a1', '96.bb1.a1', '96.bi1.a1', '144.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6499, -1, 3615, -1, 6660, -1, 4019, -1], 'generators': [577, 48, 96, 384], 'label': '1152.155815.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.j1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60973998
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.i1.a1', '24.m1.a1', '24.s1.a1', '24.u1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.be1.a1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.o1.a1', '144.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2216, -1, 7633, -1, 2874, -1, 6733, -1], 'generators': [72, 96, 384, 48], 'label': '1152.155815.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '576.8314', '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: 60973999
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.h1.a1', '24.l1.a1', '24.o1.a1', '24.v1.a1', '24.bi1.a1', '24.bj1.a1'], 'contains': ['96.d1.a1', '96.o1.a1', '144.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5669, -1, 4241, -1, 5548, -1, 5253, -1], 'generators': [648, 96, 384, 48], 'label': '1152.155815.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '576.8314', '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: 60974000
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.p1.a1', '24.z1.a1', '24.bi1.a1', '24.bk1.a1', '24.bl1.a1', '24.bw1.a1'], 'contains': ['96.d1.a1', '96.p1.a1', '96.q1.a1', '144.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5292, -1, 4850, -1, 4598, -1, 5789, -1], 'generators': [85, 96, 48, 384], 'label': '1152.155815.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '48.m1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974001
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.g1.a1', '24.l1.a1', '24.t1.a1', '24.x1.a1', '24.ba1.a1', '24.bp1.a1'], 'contains': ['96.d1.a1', '96.bj1.a1', '144.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6775, -1, 3465, -1, 7041, -1, 2624, -1], 'generators': [578, 48, 384, 96], 'label': '1152.155815.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.n1.a1', 'projective_image': '576.8314', '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': '8.5'}
  • id: 60974002
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.w1.a1', '24.bb1.a1', '24.bk1.a1', '24.bl1.a1', '24.bm1.a1', '24.br1.a1'], 'contains': ['96.d1.a1', '96.bk1.a1', '144.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5456, -1, 4512, -1, 5299, -1, 3444, -1], 'generators': [582, 48, 384, 672], 'label': '1152.155815.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '48.o1.a1', 'projective_image': '576.8314', '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': '8.5'}
  • id: 60974003
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.r1.a1', '24.w1.a1', '24.bc1.a1', '24.bi1.a1', '24.bm1.a1', '24.bw1.a1'], 'contains': ['96.d1.a1', '96.q1.a1', '144.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5042, -1, 4973, -1, 4904, -1, 5674, -1], 'generators': [661, 96, 48, 384], 'label': '1152.155815.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '48.p1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974004
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.j1.a1', '24.q1.a1', '24.bd1.a1', '24.bj1.a1', '24.bk1.a1', '24.bt1.a1'], 'contains': ['96.d1.a1', '96.bl1.a1', '144.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5860, -1, 4164, -1, 6208, -1, 2757, -1], 'generators': [579, 48, 96, 384], 'label': '1152.155815.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.q1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974005
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.p1.a1', '24.u1.a1', '24.x1.a1', '24.bj1.a1', '24.bm1.a1', '24.bx1.a1'], 'contains': ['96.d1.a1', '96.r1.a1', '144.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5734, -1, 4304, -1, 5470, -1, 4785, -1], 'generators': [75, 96, 48, 384], 'label': '1152.155815.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.r1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974006
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.k1.a1', '24.r1.a1', '24.v1.a1', '24.bd1.a1', '24.bl1.a1', '24.bx1.a1'], 'contains': ['96.d1.a1', '96.bc1.a1', '144.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5939, -1, 4100, -1, 5797, -1, 4432, -1], 'generators': [651, 96, 144, 384], 'label': '1152.155815.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.s1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974007
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.z1.a1', '12.ba1.a1', '12.bb1.a1', '12.be1.a1', '12.bf1.a1', '12.bi1.a1', '12.bj1.a1', '18.h1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2187, -1, 7048, -1, 2997, -1, 7047, -1], 'generators': [577, 48, 96, 578, 384, 12, 24], 'label': '1152.155815.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974008
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.bv1.a1', '24.ca1.a1', '24.cb1.a1'], 'contains': ['96.bm1.a1', '144.a1.a1', '192.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7772, -1, 2875, -1, 7377, -1, 1807, -1], 'generators': [48, 416, 96, 576], 'label': '1152.155815.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '48.t1.a1', 'projective_image': '576.8314', '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': '24.12'}
  • id: 60974009
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '16.b1.a1', '24.cc1.a1'], 'contains': ['96.e1.a1', '96.h1.a1', '96.l1.a1', '96.bn1.a1', '96.bn1.a2', '144.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9571, -1, 559, -1, 9383, -1, 1589, -1], 'generators': [1, 2, 48, 32], 'label': '1152.155815.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '48.u1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974010
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '16.c1.a1', '24.cc1.a1'], 'contains': ['96.e1.a1', '96.h1.a1', '96.u1.a1', '144.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8979, -1, 1179, -1, 9196, -1, 2252, -1], 'generators': [73, 2, 48, 32], 'label': '1152.155815.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '48.v1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974011
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '16.d1.a1', '24.cc1.a1', '24.cd1.a1', '24.ce1.a1'], 'contains': ['96.e1.a1', '96.s1.a1', '144.t1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5366, -1, 5074, -1, 8230, -1, 3697, -1], 'generators': [1, 72, 32, 48], 'label': '1152.155815.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.w1.a1', 'projective_image': '576.8314', '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': '16.11'}
  • id: 60974012
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.d1.a1', '24.cf1.a1', '24.cg1.a1'], 'contains': ['96.f1.a1', '96.g1.a1', '96.k1.a1', '96.bo1.a1', '96.bo1.a2', '144.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4624, -1, 5785, -1, 4140, -1, 3195, -1], 'generators': [1, 2, 48, 384], 'label': '1152.155815.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '48.x1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974013
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.e1.a1', '24.cf1.a1', '24.cg1.a1'], 'contains': ['96.f1.a1', '96.g1.a1', '96.r1.a1', '144.r1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4250, -1, 5919, -1, 4082, -1, 4600, -1], 'generators': [73, 2, 48, 384], 'label': '1152.155815.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '48.y1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974014
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.a1', '24.cf1.a1'], 'contains': ['96.f1.a1', '96.n1.a1', '96.o1.a1', '144.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3626, -1, 6213, -1, 3783, -1, 5460, -1], 'generators': [1, 168, 48, 384], 'label': '1152.155815.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.z1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974015
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.cf1.a1', '24.cl1.a1'], 'contains': ['96.g1.a1', '96.k1.a1', '96.n1.a1', '96.bp1.a1', '96.bp1.a2', '144.u1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3300, -1, 6100, -1, 3980, -1, 3823, -1], 'generators': [97, 2, 48, 384], 'label': '1152.155815.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '48.ba1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974016
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.cf1.a1', '24.cl1.a1'], 'contains': ['96.g1.a1', '96.n1.a1', '96.r1.a1', '144.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3224, -1, 6179, -1, 3481, -1, 5350, -1], 'generators': [169, 2, 48, 384], 'label': '1152.155815.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '48.bb1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974017
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.m1.a1', '24.cg1.a1', '24.cj1.a1', '24.ck1.a1', '24.cl1.a1', '24.cm1.a1', '24.cn1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '144.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [318, -1, 8626, -1, 2207, -1, 7161, -1], 'generators': [2, 72, 384, 48], 'label': '1152.155815.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bc1.a1', 'projective_image': '576.8314', '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': '16.11'}
  • id: 60974018
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1', '12.by1.a1', '18.i1.a1', '24.cc1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7574, -1, 2869, -1, 8435, -1, 2877, -1], 'generators': [1, 96, 32, 2, 576, 72, 48], 'label': '1152.155815.6.k1.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.k1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60974019
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.cf1.a1', '24.co1.a1'], 'contains': ['96.g1.a1', '96.o1.a1', '144.x1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2822, -1, 6782, -1, 2803, -1, 6199, -1], 'generators': [2, 168, 384, 48], 'label': '1152.155815.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bd1.a1', 'projective_image': '576.8314', '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': '16.11'}
  • id: 60974020
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.e1.a1', '24.cc1.a1', '24.cp1.a1', '24.cq1.a1'], 'contains': ['96.h1.a1', '96.s1.a1', '144.w1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7404, -1, 2976, -1, 8176, -1, 3608, -1], 'generators': [2, 72, 48, 32], 'label': '1152.155815.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.be1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974021
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.n1.a1', '24.cr1.a1', '24.ct1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.p1.a1', '144.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3046, -1, 8540, -1, 2153, -1, 5732, -1], 'generators': [85, 6, 48, 384], 'label': '1152.155815.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.bf1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974022
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.cs1.a1', '24.ct1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.q1.a1', '144.z1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [849, -1, 9483, -1, 1095, -1, 6441, -1], 'generators': [757, 6, 48, 384], 'label': '1152.155815.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.bg1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974023
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.p1.a1', '24.cr1.a1', '24.ct1.a1'], 'contains': ['96.i1.a1', '96.p1.a1', '96.r1.a1', '144.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2747, -1, 8490, -1, 1964, -1, 6132, -1], 'generators': [61, 6, 48, 384], 'label': '1152.155815.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.bh1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974024
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.cs1.a1', '24.ct1.a1'], 'contains': ['96.i1.a1', '96.q1.a1', '96.r1.a1', '144.bb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [714, -1, 9532, -1, 1034, -1, 6498, -1], 'generators': [733, 6, 48, 384], 'label': '1152.155815.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.bi1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974025
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.s1.a1', '24.ch1.a1', '24.cj1.a1', '24.ck1.a1', '24.cr1.a1', '24.cs1.a1', '24.cu1.a1'], 'contains': ['96.a1.a1', '96.i1.a1', '144.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [789, -1, 9734, -1, 1215, -1, 7498, -1], 'generators': [6, 72, 384, 48], 'label': '1152.155815.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bj1.a1', 'projective_image': '576.8314', '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': '16.11'}
  • id: 60974026
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.ct1.a1', '24.cv1.a1'], 'contains': ['96.i1.a1', '96.o1.a1', '144.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [895, -1, 9217, -1, 1150, -1, 6919, -1], 'generators': [6, 744, 384, 48], 'label': '1152.155815.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '48.bk1.a1', 'projective_image': '576.8314', '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': '16.11'}
  • id: 60974027
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '16.f1.a1', '24.cw1.a1'], 'contains': ['96.j1.a1', '96.l1.a1', '96.t1.a1', '144.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8821, -1, 1284, -1, 7969, -1, 2421, -1], 'generators': [85, 6, 48, 32], 'label': '1152.155815.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cw1.a1', 'old_label': '48.bl1.a1', 'projective_image': '576.8314', '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': '24.14'}
  • id: 60974028
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '16.g1.a1', '24.cw1.a1'], 'contains': ['96.j1.a1', '96.t1.a1', '96.u1.a1', '144.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8717, -1, 2211, -1, 7634, -1, 2958, -1], 'generators': [61, 6, 48, 32], 'label': '1152.155815.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cw1.a1', 'old_label': '48.bm1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974029
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bo1.a1', '12.cc1.a1', '18.j1.a1', '24.cd1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5188, -1, 4940, -1, 7470, -1, 3929, -1], 'generators': [1, 672, 32, 6, 576, 72, 48], 'label': '1152.155815.6.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.l1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60974030
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.h1.a1', '24.cd1.a1', '24.cp1.a1', '24.cw1.a1'], 'contains': ['96.j1.a1', '96.s1.a1', '144.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7137, -1, 3010, -1, 7504, -1, 3647, -1], 'generators': [6, 72, 48, 32], 'label': '1152.155815.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.bn1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974031
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.u1.a1', '24.cg1.a1', '24.cl1.a1', '24.cr1.a1', '24.cs1.a1', '24.cx1.a1', '24.cy1.a1'], 'contains': ['96.a1.a1', '96.k1.a1', '96.r1.a1', '144.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1126, -1, 9121, -1, 2035, -1, 6799, -1], 'generators': [3, 72, 48, 384], 'label': '1152.155815.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bo1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974032
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.cf1.a1', '24.ct1.a1'], 'contains': ['96.k1.a1', '96.o1.a1', '96.r1.a1', '144.bf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [948, -1, 7136, -1, 2099, -1, 6066, -1], 'generators': [3, 168, 48, 384], 'label': '1152.155815.48.bp1.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.bp1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974033
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '16.i1.a1', '24.cc1.a1', '24.cw1.a1', '24.cz1.a1'], 'contains': ['96.l1.a1', '96.s1.a1', '96.u1.a1', '144.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7885, -1, 2525, -1, 7915, -1, 3328, -1], 'generators': [3, 72, 48, 32], 'label': '1152.155815.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.bq1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974034
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '16.i1.a1', '24.da1.a1'], 'contains': ['96.m1.a1', '96.v1.a1', '96.w1.a1', '144.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6090, -1, 5407, -1, 5998, -1, 4266, -1], 'generators': [3, 72, 48, 416], 'label': '1152.155815.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1.a1', 'old_label': '48.br1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974035
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.y1.a1', '24.cl1.a1', '24.cu1.a1', '24.db1.a1', '24.dc1.a1', '24.dd1.a1'], 'contains': ['96.a1.a1', '96.n1.a1', '144.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1082, -1, 8248, -1, 1484, -1, 8254, -1], 'generators': [97, 72, 48, 384], 'label': '1152.155815.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bs1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60974036
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.y1.a1', '24.cv1.a1'], 'contains': ['96.n1.a1', '96.o1.a1', '144.bh1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1801, -1, 7724, -1, 2708, -1, 6249, -1], 'generators': [577, 168, 48, 384], 'label': '1152.155815.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.bt1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60974037
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.bc1.a1', '24.ci1.a1', '24.cn1.a1', '24.cs1.a1', '24.dc1.a1', '24.dd1.a1'], 'contains': ['96.a1.a1', '96.q1.a1', '144.bj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1410, -1, 8213, -1, 1311, -1, 8455, -1], 'generators': [181, 72, 48, 384], 'label': '1152.155815.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bu1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60974038
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '24.bf1.a1', '24.ci1.a1', '24.ck1.a1', '24.cy1.a1', '24.db1.a1', '24.dd1.a1'], 'contains': ['96.a1.a1', '144.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [377, -1, 9347, -1, 1268, -1, 9274, -1], 'generators': [108, 384, 24, 48], 'label': '1152.155815.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bv1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974039
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bh1.a1', '24.ch1.a1', '24.cm1.a1', '24.cn1.a1', '24.cu1.a1', '24.cx1.a1', '24.cy1.a1'], 'contains': ['96.a1.a1', '144.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [14, -1, 9778, -1, 1397, -1, 8213, -1], 'generators': [7, 24, 48, 384], 'label': '1152.155815.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bw1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974040
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.bo1.a1', '12.cb1.a1', '18.k1.a1', '24.ce1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5127, -1, 5376, -1, 7204, -1, 3725, -1], 'generators': [1, 96, 48, 12, 576, 32, 24], 'label': '1152.155815.6.m1.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.m1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60974041
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.bi1.a1', '24.ct1.a1'], 'contains': ['96.o1.a1', '96.p1.a1', '96.q1.a1', '144.bm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3093, -1, 7888, -1, 1766, -1, 6556, -1], 'generators': [85, 168, 48, 384], 'label': '1152.155815.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '48.bx1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974043
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.co1.a1', '24.cv1.a1'], 'contains': ['96.o1.a1', '144.bo1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2346, -1, 7034, -1, 1723, -1, 7313, -1], 'generators': [103, 696, 48, 384], 'label': '1152.155815.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '48.bz1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974044
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '16.j1.a1', '24.ce1.a1', '24.cq1.a1', '24.cw1.a1'], 'contains': ['96.s1.a1', '96.t1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7212, -1, 3126, -1, 7251, -1, 3758, -1], 'generators': [85, 72, 32, 48], 'label': '1152.155815.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.ca1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974045
    {'ambient': '1152.155815', 'aut_centralizer_order': 144, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '16.k1.a1', '24.ce1.a1', '24.cp1.a1', '24.cz1.a1'], 'contains': ['96.s1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4806, -1, 5522, -1, 6430, -1, 5096, -1], 'generators': [12, 32, 24, 48], 'label': '1152.155815.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.cb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974046
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1.a1', '16.l1.a1', '24.cd1.a1', '24.cq1.a1', '24.cz1.a1'], 'contains': ['96.s1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4931, -1, 5306, -1, 6388, -1, 5136, -1], 'generators': [7, 24, 48, 32], 'label': '1152.155815.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.cc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974047
    {'ambient': '1152.155815', 'aut_centralizer_order': 72, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '16.k1.a1', '24.da1.a1'], 'contains': ['96.v1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4465, -1, 8057, -1, 4538, -1, 5975, -1], 'generators': [12, 416, 24, 48], 'label': '1152.155815.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '48.cd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974048
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '16.l1.a1', '24.da1.a1'], 'contains': ['96.v1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4500, -1, 8106, -1, 4495, -1, 6015, -1], 'generators': [7, 24, 48, 416], 'label': '1152.155815.48.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1.a1', 'old_label': '48.ce1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974049
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1'], 'contains': ['96.x1.a1', '96.y1.a1', '96.ba1.a1', '96.bo1.a1', '96.bo1.a2', '96.bp1.a1', '96.bp1.a2', '144.bp1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7039, -1, 3182, -1, 7446, -1, 2367, -1], 'generators': [1, 2, 144, 384], 'label': '1152.155815.48.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '48.cf1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974050
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1'], 'contains': ['96.y1.a1', '96.bb1.a1', '96.bc1.a1', '144.bq1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6990, -1, 3243, -1, 7323, -1, 3894, -1], 'generators': [649, 2, 144, 384], 'label': '1152.155815.48.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1.a1', 'old_label': '48.cg1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974051
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.l1.a1', '12.p1.a1', '12.z1.a1', '12.bp1.a1', '12.bq1.a1', '12.br1.a1', '12.bx1.a1', '18.i1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4770, -1, 4738, -1, 5653, -1, 4866, -1], 'generators': [1, 96, 48, 2, 384, 72, 576], 'label': '1152.155815.6.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.n1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974052
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '24.de1.a1', '24.de1.a2'], 'contains': ['96.x1.a1', '96.bb1.a1', '96.bd1.a1', '96.be1.a1', '96.bi1.a1', '144.br1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8166, -1, 2083, -1, 8741, -1, 1427, -1], 'generators': [1, 624, 96, 384], 'label': '1152.155815.48.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.ch1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974053
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '24.de1.a1', '24.de1.a2'], 'contains': ['96.bd1.a1', '96.bf1.a1', '96.bj1.a1', '144.bs1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8395, -1, 1910, -1, 8927, -1, 1163, -1], 'generators': [2, 624, 384, 96], 'label': '1152.155815.48.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.ci1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974054
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1'], 'contains': ['96.bd1.a1', '96.bg1.a1', '96.bk1.a1', '144.bt1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7509, -1, 2649, -1, 6333, -1, 2094, -1], 'generators': [6, 624, 384, 672], 'label': '1152.155815.48.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '48.cj1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974055
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.de1.a1', '24.de1.a2'], 'contains': ['96.bd1.a1', '96.bh1.a1', '96.bl1.a1', '144.bu1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8230, -1, 1738, -1, 8873, -1, 1112, -1], 'generators': [3, 624, 96, 384], 'label': '1152.155815.48.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.ck1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974056
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.de1.a1', '24.dg1.a1'], 'contains': ['96.be1.a1', '96.bf1.a1', '96.bh1.a1', '96.bo1.a1', '96.bp1.a1', '144.bv1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8286, -1, 1995, -1, 8814, -1, 1297, -1], 'generators': [1, 2, 96, 384], 'label': '1152.155815.48.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cl1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974057
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.de1.a2', '24.dg1.a2'], 'contains': ['96.be1.a1', '96.bf1.a1', '96.bh1.a1', '96.bo1.a2', '96.bp1.a2', '144.bv1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8286, -1, 1854, -1, 8814, -1, 1228, -1], 'generators': [49, 2, 96, 384], 'label': '1152.155815.48.cl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cl1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974058
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.de1.a1', '24.dg1.a2'], 'contains': ['96.be1.a1', '96.bj1.a1', '96.bl1.a1', '144.bw1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8610, -1, 1489, -1, 9100, -1, 732, -1], 'generators': [49, 578, 96, 384], 'label': '1152.155815.48.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cm1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974059
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.de1.a2', '24.dg1.a1'], 'contains': ['96.be1.a1', '96.bj1.a1', '96.bl1.a1', '144.bw1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8610, -1, 1438, -1, 9100, -1, 673, -1], 'generators': [1, 578, 96, 384], 'label': '1152.155815.48.cm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cm1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974060
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.de1.a1', '24.dg1.a2'], 'contains': ['96.bf1.a1', '96.bi1.a1', '96.bl1.a1', '144.bx1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8485, -1, 1773, -1, 8982, -1, 1023, -1], 'generators': [625, 2, 96, 384], 'label': '1152.155815.48.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cn1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974061
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.de1.a2', '24.dg1.a1'], 'contains': ['96.bf1.a1', '96.bi1.a1', '96.bl1.a1', '144.bx1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8485, -1, 1575, -1, 8982, -1, 982, -1], 'generators': [577, 2, 96, 384], 'label': '1152.155815.48.cn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cn1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974062
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.j1.a1', '12.m1.a1', '12.w1.a1', '12.be1.a1', '12.bu1.a1', '12.ca1.a1', '18.j1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3870, -1, 6407, -1, 3818, -1, 6779, -1], 'generators': [1, 48, 672, 6, 384, 576, 72], 'label': '1152.155815.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.o1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974063
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.de1.a1', '24.dg1.a1'], 'contains': ['96.bh1.a1', '96.bi1.a1', '96.bj1.a1', '144.by1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8566, -1, 1807, -1, 9153, -1, 881, -1], 'generators': [577, 578, 96, 384], 'label': '1152.155815.48.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.co1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974064
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.de1.a2', '24.dg1.a2'], 'contains': ['96.bh1.a1', '96.bi1.a1', '96.bj1.a1', '144.by1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8566, -1, 1532, -1, 9153, -1, 842, -1], 'generators': [625, 578, 96, 384], 'label': '1152.155815.48.co1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.co1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974065
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.bn1.a1', '24.df1.a1', '24.df1.a2'], 'contains': ['96.c1.a1', '144.bz1.a1', '192.f1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9740, -1, 242, -1, 9924, -1, 26, -1], 'generators': [1, 32, 96, 576], 'label': '1152.155815.48.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '48.cp1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974066
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.bo1.a1', '24.dg1.a1', '24.dg1.a2'], 'contains': ['96.b1.a1', '96.be1.a1', '96.bi1.a1', '144.bz1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8914, -1, 805, -1, 9536, -1, 608, -1], 'generators': [1, 96, 576, 384], 'label': '1152.155815.48.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.cq1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60974067
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bp1.a1', '24.dg1.a1', '24.dg1.a2'], 'contains': ['96.b1.a1', '96.bf1.a1', '96.bj1.a1', '144.ca1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9394, -1, 701, -1, 9606, -1, 543, -1], 'generators': [2, 576, 384, 96], 'label': '1152.155815.48.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cr1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974068
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bq1.a1', '24.df1.a1', '24.df1.a2'], 'contains': ['96.c1.a1', '144.ca1.a1', '192.i1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9645, -1, 64, -1, 9973, -1, 104, -1], 'generators': [2, 32, 96, 576], 'label': '1152.155815.48.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.cs1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974069
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.br1.a1'], 'contains': ['96.b1.a1', '96.bg1.a1', '96.bk1.a1', '144.cb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8663, -1, 1386, -1, 7852, -1, 1362, -1], 'generators': [6, 576, 384, 672], 'label': '1152.155815.48.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '48.ct1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974070
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '96.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.bs1.a1'], 'contains': ['96.c1.a1', '144.cb1.a1', '192.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9226, -1, 617, -1, 8669, -1, 1076, -1], 'generators': [6, 32, 672, 576], 'label': '1152.155815.48.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.cu1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974071
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '24.bt1.a1', '24.dg1.a1', '24.dg1.a2'], 'contains': ['96.b1.a1', '96.bh1.a1', '96.bl1.a1', '144.cc1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9348, -1, 744, -1, 9478, -1, 492, -1], 'generators': [3, 576, 96, 384], 'label': '1152.155815.48.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.cv1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60974072
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '144.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '24.bu1.a1', '24.df1.a1', '24.df1.a2'], 'contains': ['96.c1.a1', '144.cc1.a1', '192.m1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9816, -1, 282, -1, 9836, -1, 72, -1], 'generators': [3, 32, 96, 576], 'label': '1152.155815.48.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.cw1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974073
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.o1.a1', '12.r1.a1', '12.x1.a1', '12.bi1.a1', '12.br1.a1', '12.bu1.a1', '18.l1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4114, -1, 6337, -1, 3963, -1, 6636, -1], 'generators': [2, 96, 72, 12, 48, 576, 384], 'label': '1152.155815.6.p1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.p1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60974074
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '24.bv1.a1'], 'contains': ['96.bm1.a1', '144.cc1.a1', '192.n1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9011, -1, 1211, -1, 9720, -1, 335, -1], 'generators': [3, 416, 96, 576], 'label': '1152.155815.48.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bz1.a1', 'old_label': '48.cx1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974075
    {'ambient': '1152.155815', 'aut_centralizer_order': 288, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1'], 'contains': ['128.a1.a1', '192.a1.a1', '192.b1.a1', '192.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9177, -1, 935, -1, 8287, -1, 2253, -1], 'generators': [48, 32, 384], 'label': '1152.155815.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.a1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974076
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '32.b1.a1', '32.i1.a1', '32.i1.a2'], 'contains': ['128.a1.a1', '192.f1.a1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9986, -1, 239, -1, 9559, -1, 431, -1], 'generators': [1, 32, 384], 'label': '1152.155815.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '64.b1.a1', 'projective_image': '1152.155815', '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': '12.4'}
  • id: 60974077
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '32.c1.a1', '32.i1.a1', '32.i1.a2'], 'contains': ['128.a1.a1', '192.h1.a1', '192.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9881, -1, 144, -1, 9496, -1, 531, -1], 'generators': [2, 384, 32], 'label': '1152.155815.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '64.c1.a1', 'projective_image': '1152.155815', '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': '12.4'}
  • id: 60974078
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '32.d1.a1'], 'contains': ['128.a1.a1', '192.j1.a1', '192.k1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9530, -1, 637, -1, 8421, -1, 1571, -1], 'generators': [6, 384, 32], 'label': '1152.155815.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '64.d1.a1', 'projective_image': '1152.155815', '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': '12.4'}
  • id: 60974079
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '32.e1.a1', '32.i1.a1', '32.i1.a2'], 'contains': ['128.a1.a1', '192.l1.a1', '192.m1.a1', '192.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9942, -1, 14, -1, 9390, -1, 481, -1], 'generators': [3, 32, 384], 'label': '1152.155815.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '64.e1.a1', 'projective_image': '1152.155815', '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': '36.10'}
  • id: 60974080
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.ca1.a1', '36.a1.a1', '36.bj1.a1', '36.bk1.a1', '36.bn1.a1', '36.bo1.a1', '36.bp1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.h1.a1', '144.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4703, 4644, 5363, 5633, 5375, 3508, 5406, 5473], 'generators': [72, 96, 576], 'label': '1152.155815.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974081
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1', '36.d1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.f1.a1', '144.q1.a1', '144.u1.a1', '144.bp1.a1', '144.bv1.a1', '144.bv1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6611, -1, 3560, -1, 6865, -1, 3023, -1], 'generators': [1, 2, 48, 96], 'label': '1152.155815.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974082
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1', '36.d1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.o1.a1', '144.r1.a1', '144.v1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6174, -1, 4105, -1, 5934, -1, 4549, -1], 'generators': [73, 2, 96], 'label': '1152.155815.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974083
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.c1.a1', '36.g1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.k1.a1', '144.n1.a1', '144.bw1.a1', '144.bw1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6673, -1, 3500, -1, 7181, -1, 2492, -1], 'generators': [1, 578, 48], 'label': '1152.155815.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974084
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.q1.a1', '12.s1.a1', '12.bg1.a1', '12.bj1.a1', '12.br1.a1', '12.ca1.a1', '18.m1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4029, -1, 6172, -1, 3719, -1, 7199, -1], 'generators': [85, 48, 96, 2, 384, 576, 72], 'label': '1152.155815.6.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.q1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60974085
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.b1.a1', '36.g1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.k1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6726, -1, 3597, -1, 6976, -1, 3383, -1], 'generators': [73, 578], 'label': '1152.155815.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974086
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.b1.a1', '36.c1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.g1.a1', '144.i1.a1', '144.s1.a1', '144.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6068, -1, 4053, -1, 5869, -1, 5187, -1], 'generators': [1, 648, 96], 'label': '1152.155815.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974087
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.i1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.h1.a1', '144.s1.a1', '144.t1.a1', '144.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3780, -1, 6442, -1, 3664, -1, 6859, -1], 'generators': [1, 72, 96], 'label': '1152.155815.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974088
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.c1.a1', '36.k1.a1', '36.bh1.a1'], 'contains': ['144.d1.a1', '144.g1.a1', '144.n1.a1', '144.bx1.a1', '144.bx1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6499, -1, 3674, -1, 6916, -1, 2690, -1], 'generators': [577, 2, 48], 'label': '1152.155815.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.h1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974089
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.b1.a1', '36.k1.a1', '36.bi1.a1'], 'contains': ['144.d1.a1', '144.g1.a1', '144.p1.a1', '144.bq1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6553, -1, 3727, -1, 6590, -1, 4206, -1], 'generators': [649, 2, 96], 'label': '1152.155815.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.i1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974090
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.b1.a1', '36.c1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.i1.a1', '144.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6239, -1, 4006, -1, 6531, -1, 4320, -1], 'generators': [2, 648], 'label': '1152.155815.72.j1.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': '72.j1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974091
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.d1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.h1.a1', '144.w1.a1', '144.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2821, -1, 6853, -1, 3600, -1, 6667, -1], 'generators': [2, 72, 96], 'label': '1152.155815.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974092
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.o1.a1', '36.q1.a1', '36.bl1.a1'], 'contains': ['144.e1.a1', '144.f1.a1', '144.j1.a1', '144.y1.a1', '144.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5409, -1, 4745, -1, 4735, -1, 5607, -1], 'generators': [85, 6, 672], 'label': '1152.155815.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974093
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.o1.a1', '36.p1.a1', '36.bn1.a1'], 'contains': ['144.e1.a1', '144.i1.a1', '144.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5300, -1, 4837, -1, 5234, -1, 4933, -1], 'generators': [6, 648], 'label': '1152.155815.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '72.m1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974094
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.p1.a1', '36.q1.a1', '36.bm1.a1'], 'contains': ['144.e1.a1', '144.j1.a1', '144.o1.a1', '144.ba1.a1', '144.bb1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5036, -1, 5054, -1, 4437, -1, 5861, -1], 'generators': [61, 6, 672], 'label': '1152.155815.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.n1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974095
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.e1.a1', '576.f1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.f1.a1', '6.a1.a1', '6.m1.a1', '8.j1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5247, 1622, 5189, 8902, 7200, 1937, 3837, 8091], 'generators': [1, 48, 672, 12, 24, 384, 576, 32], 'label': '1152.155815.2.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.e1.a1', '4.f1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60974096
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.cb1.a1', '12.cc1.a1', '18.m1.a1', '24.cq1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6685, -1, 4613, -1, 7110, -1, 3637, -1], 'generators': [85, 96, 32, 2, 576, 72, 48], 'label': '1152.155815.6.r1.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.r1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60974097
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.p1.a1', '36.t1.a1', '36.bl1.a1'], 'contains': ['144.e1.a1', '144.m1.a1', '144.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5173, -1, 4698, -1, 4970, -1, 5052, -1], 'generators': [661, 6], 'label': '1152.155815.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.o1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974098
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.o1.a1', '36.t1.a1', '36.bm1.a1'], 'contains': ['144.e1.a1', '144.m1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5510, -1, 4620, -1, 4838, -1, 4883, -1], 'generators': [637, 6], 'label': '1152.155815.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.p1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974099
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.e1.a1', '36.j1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '36.bn1.a1'], 'contains': ['144.e1.a1', '144.h1.a1', '144.bc1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1884, -1, 8719, -1, 2945, -1, 7396, -1], 'generators': [6, 72, 672], 'label': '1152.155815.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.q1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974100
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.b1.a1', '36.u1.a1', '36.bh1.a1'], 'contains': ['144.f1.a1', '144.g1.a1', '144.k1.a1', '144.by1.a1', '144.by1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6791, -1, 3429, -1, 7112, -1, 2557, -1], 'generators': [577, 578, 48], 'label': '1152.155815.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.r1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974101
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '36.d1.a1', '36.q1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1', '36.x1.a1', '36.bo1.a1'], 'contains': ['144.f1.a1', '144.h1.a1', '144.o1.a1', '144.be1.a1', '144.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2548, -1, 7089, -1, 3906, -1, 6385, -1], 'generators': [3, 72, 96], 'label': '1152.155815.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.s1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974102
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '36.b1.a1', '36.o1.a1', '36.bo1.a1'], 'contains': ['144.f1.a1', '144.i1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5958, -1, 4337, -1, 5731, -1, 4494, -1], 'generators': [3, 648], 'label': '1152.155815.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974103
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '36.o1.a1', '36.v1.a1', '36.bl1.a1'], 'contains': ['144.f1.a1', '144.l1.a1', '144.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5588, -1, 4530, -1, 5137, -1, 3546, -1], 'generators': [661, 582], 'label': '1152.155815.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.u1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974104
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '36.c1.a1', '36.u1.a1', '36.bi1.a1'], 'contains': ['144.g1.a1', '144.k1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6126, -1, 3789, -1, 6478, -1, 4370, -1], 'generators': [649, 578], 'label': '1152.155815.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.v1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974105
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.k1.a1', '36.r1.a1', '36.u1.a1', '36.y1.a1', '36.z1.a1', '36.ba1.a1', '36.bj1.a1'], 'contains': ['144.g1.a1', '144.h1.a1', '144.bg1.a1', '144.bh1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2031, -1, 7521, -1, 3362, -1, 7062, -1], 'generators': [577, 72, 96], 'label': '1152.155815.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.w1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974106
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '36.f1.a1', '36.l1.a1', '36.q1.a1', '36.y1.a1', '36.bb1.a1', '36.bc1.a1', '36.bp1.a1'], 'contains': ['144.h1.a1', '144.j1.a1', '144.bi1.a1', '144.bj1.a1', '144.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3567, -1, 6934, -1, 3075, -1, 7558, -1], 'generators': [85, 72, 96], 'label': '1152.155815.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.x1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974107
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '12.y1.a1', '12.ba1.a1', '12.bh1.a1', '12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '12.bx1.a1', '18.n1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4609, -1, 4813, -1, 4908, -1, 5065, -1], 'generators': [85, 672, 48, 6, 384, 72, 576], 'label': '1152.155815.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.s1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60974108
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '36.g1.a1', '36.s1.a1', '36.u1.a1', '36.bb1.a1', '36.bd1.a1', '36.be1.a1', '36.bk1.a1'], 'contains': ['144.h1.a1', '144.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3911, -1, 5774, -1, 4038, -1, 6330, -1], 'generators': [578, 72], 'label': '1152.155815.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.y1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974109
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '36.h1.a1', '36.m1.a1', '36.v1.a1', '36.z1.a1', '36.bc1.a1', '36.bd1.a1', '36.bn1.a1'], 'contains': ['144.h1.a1', '144.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3975, -1, 5644, -1, 4199, -1, 6290, -1], 'generators': [582, 72], 'label': '1152.155815.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.z1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974110
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '36.i1.a1', '36.n1.a1', '36.t1.a1', '36.v1.a1', '36.ba1.a1', '36.be1.a1', '36.bp1.a1'], 'contains': ['144.h1.a1', '144.m1.a1', '144.bj1.a1', '144.bn1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2620, -1, 7249, -1, 3729, -1, 7619, -1], 'generators': [661, 72, 96], 'label': '1152.155815.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974111
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '36.g1.a1', '36.k1.a1', '36.t1.a1', '36.bc1.a1', '36.bf1.a1', '36.bg1.a1', '36.bo1.a1'], 'contains': ['144.h1.a1', '144.n1.a1', '144.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3067, -1, 7615, -1, 4240, -1, 5498, -1], 'generators': [579, 72], 'label': '1152.155815.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974112
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.a1.a1', '36.f1.a1', '36.j1.a1', '36.w1.a1', '36.ba1.a1', '36.bd1.a1', '36.bf1.a1'], 'contains': ['144.b1.a1', '144.h1.a1', '144.bk1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2950, -1, 7862, -1, 3233, -1, 8404, -1], 'generators': [12, 96], 'label': '1152.155815.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974113
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '36.a1.a1', '36.i1.a1', '36.m1.a1', '36.s1.a1', '36.x1.a1', '36.y1.a1', '36.bg1.a1'], 'contains': ['144.h1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2158, -1, 8633, -1, 3297, -1, 8344, -1], 'generators': [588, 96], 'label': '1152.155815.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974114
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '36.h1.a1', '36.n1.a1', '36.r1.a1', '36.x1.a1', '36.bb1.a1', '36.bf1.a1', '36.bq1.a1'], 'contains': ['144.h1.a1', '144.bo1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3492, -1, 6781, -1, 3427, -1, 7722, -1], 'generators': [583, 672], 'label': '1152.155815.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.be1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974115
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '36.e1.a1', '36.l1.a1', '36.w1.a1', '36.z1.a1', '36.be1.a1', '36.bg1.a1', '36.bq1.a1'], 'contains': ['144.h1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1308, -1, 8806, -1, 3010, -1, 8048, -1], 'generators': [7, 672], 'label': '1152.155815.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974116
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.o1.a1', '36.p1.a1', '36.bp1.a1'], 'contains': ['144.i1.a1', '144.j1.a1', '144.m1.a1', '144.bm1.a1', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4977, -1, 4998, -1, 4670, -1, 5926, -1], 'generators': [85, 648, 96], 'label': '1152.155815.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.bg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974117
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '36.c1.a1', '36.p1.a1', '36.bo1.a1'], 'contains': ['144.i1.a1', '144.n1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5823, -1, 4405, -1, 5682, -1, 4727, -1], 'generators': [579, 648], 'label': '1152.155815.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bh1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60974118
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bv1.a1', '12.bw1.a1', '12.by1.a1', '12.cb1.a1', '18.n1.a1', '24.cw1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7135, -1, 3336, -1, 7748, -1, 3003, -1], 'generators': [85, 672, 32, 6, 576, 72, 48], 'label': '1152.155815.6.t1.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.t1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60974119
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.p1.a1', '36.bc1.a1', '36.bl1.a1'], 'contains': ['144.j1.a1', '144.l1.a1', '144.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5455, -1, 4658, -1, 5185, -1, 3500, -1], 'generators': [85, 582], 'label': '1152.155815.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.bi1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974120
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '36.o1.a1', '36.bc1.a1', '36.bm1.a1'], 'contains': ['144.j1.a1', '144.l1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5549, -1, 4568, -1, 5016, -1, 4839, -1], 'generators': [61, 582], 'label': '1152.155815.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.bj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974121
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.p1.a1', '36.v1.a1', '36.bm1.a1'], 'contains': ['144.l1.a1', '144.m1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5132, -1, 4926, -1, 4789, -1, 5310, -1], 'generators': [637, 582], 'label': '1152.155815.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '72.bk1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974122
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '24.bo1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.g1.a1', '144.br1.a1', '144.bz1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7874, -1, 2378, -1, 8335, -1, 1976, -1], 'generators': [1, 48, 96, 576], 'label': '1152.155815.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bl1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974123
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '24.bq1.a1', '36.bh1.a1', '36.bi1.a1', '36.bk1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.k1.a1', '144.bs1.a1', '144.ca1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8082, -1, 2278, -1, 8387, -1, 1927, -1], 'generators': [2, 48, 576], 'label': '1152.155815.72.bm1.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': '72.bm1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974124
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.bs1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.l1.a1', '144.bt1.a1', '144.cb1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7310, -1, 2573, -1, 6136, -1, 2824, -1], 'generators': [6, 48, 576], 'label': '1152.155815.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '72.bn1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974125
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bu1.a1', '24.bv1.a1', '36.bh1.a1', '36.bl1.a1', '36.bo1.a1'], 'contains': ['144.a1.a1', '144.f1.a1', '144.n1.a1', '144.bu1.a1', '144.cc1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7786, -1, 2492, -1, 8104, -1, 1867, -1], 'generators': [3, 48, 576], 'label': '1152.155815.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bo1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974126
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '24.by1.a1', '36.bl1.a1', '36.bm1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7253, -1, 2918, -1, 5623, -1, 4672, -1], 'generators': [85, 96, 576], 'label': '1152.155815.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.bp1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974127
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '24.bz1.a1', '24.cb1.a1', '36.bi1.a1', '36.bm1.a1', '36.bo1.a1'], 'contains': ['144.a1.a1', '144.o1.a1', '144.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7543, -1, 2824, -1, 6274, -1, 4078, -1], 'generators': [75, 576], 'label': '1152.155815.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bq1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974128
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '36.d1.a1'], 'contains': ['144.q1.a1', '144.r1.a1', '144.s1.a1', '144.u1.a1', '144.v1.a1', '144.x1.a1', '144.bf1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3317, -1, 6510, -1, 3836, -1, 5547, -1], 'generators': [1, 2, 168], 'label': '1152.155815.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.br1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974129
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.bb1.a1', '12.bc1.a1', '12.bk1.a1', '12.bl1.a1', '12.bx1.a1', '12.ca1.a1', '18.o1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3369, -1, 7962, -1, 3889, -1, 7858, -1], 'generators': [3, 48, 96, 12, 384, 576, 24], 'label': '1152.155815.6.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.u1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60974130
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '24.cg1.a1', '36.d1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.q1.a1', '144.r1.a1', '144.t1.a1', '144.w1.a1', '144.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4110, -1, 6037, -1, 3535, -1, 6606, -1], 'generators': [1, 2, 72], 'label': '1152.155815.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bs1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974131
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.a1', '24.ch1.a1', '36.e1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.t1.a1', '144.bc1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1735, -1, 9136, -1, 2456, -1, 8177, -1], 'generators': [1, 6], 'label': '1152.155815.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bt1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974132
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.ce1.a1', '36.f1.a1', '36.br1.a1'], 'contains': ['144.b1.a1', '144.t1.a1', '144.bi1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4359, -1, 5935, -1, 3178, -1, 7921, -1], 'generators': [1, 12], 'label': '1152.155815.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bu1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974133
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '36.f1.a1', '36.i1.a1', '36.bs1.a1'], 'contains': ['144.t1.a1', '144.bj1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2454, -1, 8015, -1, 1901, -1, 9508, -1], 'generators': [1, 108], 'label': '1152.155815.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bv1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974134
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '24.cp1.a1', '36.j1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.w1.a1', '144.bc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2487, -1, 8289, -1, 2580, -1, 7959, -1], 'generators': [2, 12], 'label': '1152.155815.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.bw1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974135
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.j1.a1', '36.bs1.a1', '36.bt1.a1'], 'contains': ['144.w1.a1', '144.bc1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [417, -1, 9481, -1, 1522, -1, 9194, -1], 'generators': [2, 108], 'label': '1152.155815.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.bx1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974136
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.d1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.u1.a1', '144.v1.a1', '144.w1.a1', '144.be1.a1', '144.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [767, -1, 9312, -1, 2319, -1, 7222, -1], 'generators': [97, 2, 72], 'label': '1152.155815.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.by1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974137
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '24.cq1.a1', '36.l1.a1', '36.br1.a1', '36.bt1.a1'], 'contains': ['144.w1.a1', '144.bi1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [706, -1, 8588, -1, 2496, -1, 7996, -1], 'generators': [85, 2], 'label': '1152.155815.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bz1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974138
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.l1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.w1.a1', '144.bj1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [562, -1, 9372, -1, 1678, -1, 8682, -1], 'generators': [181, 2], 'label': '1152.155815.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ca1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974139
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.n1.a1'], 'contains': ['144.x1.a1', '144.bn1.a1', '144.bo1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2685, -1, 6569, -1, 2664, -1, 7671, -1], 'generators': [661, 2], 'label': '1152.155815.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.n1.a1', 'old_label': '72.cb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974140
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.by1.a1', '12.cc1.a1', '18.o1.a1', '24.cz1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4838, -1, 5815, -1, 6607, -1, 5389, -1], 'generators': [3, 96, 32, 12, 576, 24, 48], 'label': '1152.155815.6.v1.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.v1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60974141
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '24.cw1.a1', '36.q1.a1', '36.br1.a1', '36.bt1.a1'], 'contains': ['144.y1.a1', '144.ba1.a1', '144.bc1.a1', '144.be1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1956, -1, 8537, -1, 2541, -1, 7273, -1], 'generators': [85, 6, 72], 'label': '1152.155815.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974142
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.q1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.z1.a1', '144.bb1.a1', '144.bc1.a1', '144.be1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [614, -1, 9449, -1, 1354, -1, 8294, -1], 'generators': [757, 6, 72], 'label': '1152.155815.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974143
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '36.q1.a1'], 'contains': ['144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1', '144.bd1.a1', '144.bf1.a1', '144.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [872, -1, 9196, -1, 1441, -1, 6970, -1], 'generators': [85, 6, 744], 'label': '1152.155815.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '72.ce1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974144
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.e1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.bc1.a1', '144.bg1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [529, -1, 9403, -1, 1556, -1, 8644, -1], 'generators': [673, 6], 'label': '1152.155815.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974145
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.r1.a1'], 'contains': ['144.bd1.a1', '144.bh1.a1', '144.bo1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2087, -1, 8462, -1, 1590, -1, 7350, -1], 'generators': [97, 6], 'label': '1152.155815.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '72.cg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974146
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '24.cz1.a1', '24.da1.a1', '36.w1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.be1.a1', '144.bl1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3642, -1, 8964, -1, 3131, -1, 8100, -1], 'generators': [3, 12], 'label': '1152.155815.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ch1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974147
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '36.w1.a1', '36.bs1.a1', '36.bt1.a1'], 'contains': ['144.be1.a1', '144.bk1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [320, -1, 9786, -1, 1631, -1, 9232, -1], 'generators': [3, 108], 'label': '1152.155815.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ci1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60974148
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1.a1', '36.f1.a1', '36.y1.a1', '36.bt1.a1'], 'contains': ['144.bg1.a1', '144.bi1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [667, -1, 9016, -1, 1854, -1, 9322, -1], 'generators': [97, 108], 'label': '1152.155815.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974149
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '36.f1.a1', '36.ba1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.bg1.a1', '144.bj1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1783, -1, 7817, -1, 2263, -1, 9365, -1], 'generators': [97, 12], 'label': '1152.155815.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ck1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60974150
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '36.i1.a1', '36.y1.a1', '36.ba1.a1'], 'contains': ['144.bg1.a1', '144.bj1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1837, -1, 7906, -1, 2416, -1, 9582, -1], 'generators': [577, 108], 'label': '1152.155815.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1.a1', 'old_label': '72.cl1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974151
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['12.bz1.a1', '12.cd1.a1', '12.ce1.a1', '18.o1.a1', '24.da1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4304, -1, 8611, -1, 4991, -1, 5923, -1], 'generators': [3, 96, 416, 12, 576, 24, 48], 'label': '1152.155815.6.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '6.w1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60974152
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '36.bh1.a1'], 'contains': ['144.br1.a1', '144.bs1.a1', '144.bu1.a1', '144.bv1.a1', '144.bw1.a1', '144.bx1.a1', '144.by1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8420, -1, 2066, -1, 9036, -1, 931, -1], 'generators': [1, 2, 624], 'label': '1152.155815.72.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cm1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974153
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a2', '36.bh1.a1'], 'contains': ['144.br1.a1', '144.bs1.a1', '144.bu1.a1', '144.bv1.a2', '144.bw1.a2', '144.bx1.a2', '144.by1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8420, -1, 1653, -1, 9036, -1, 792, -1], 'generators': [577, 2, 624], 'label': '1152.155815.72.cm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cm1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974154
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a1', '24.dg1.a1', '36.bh1.a1'], 'contains': ['144.bv1.a1', '144.bw1.a2', '144.bx1.a2', '144.by1.a1', '144.bz1.a1', '144.ca1.a1', '144.cc1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9028, -1, 848, -1, 9670, -1, 381, -1], 'generators': [1, 2, 576], 'label': '1152.155815.72.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cn1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974155
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a2', '24.dg1.a2', '36.bh1.a1'], 'contains': ['144.bv1.a2', '144.bw1.a1', '144.bx1.a1', '144.by1.a2', '144.bz1.a1', '144.ca1.a1', '144.cc1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9028, -1, 442, -1, 9670, -1, 442, -1], 'generators': [49, 2, 576], 'label': '1152.155815.72.cn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cn1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974156
    {'ambient': '1152.155815', 'aut_centralizer_order': 1152, 'aut_label': '96.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.k1.a1', '48.bc1.a1', '48.bj1.a1', '48.bo1.a1', '48.bs1.a1', '48.bu1.a1', '48.bv1.a1', '48.bw1.a1'], 'contains': ['192.a1.a1', '288.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1745, 3040, 8335, 7094, 2207, 2832, 7347, 6739], 'generators': [72, 384, 48], 'label': '1152.155815.96.a1.a1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1'], 'normal_contains': ['192.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974157
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.e1.a1', 'complements': ['12.cf1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.cq1.a1', '48.cr1.a1', '48.ct1.a1', '48.cv1.a1'], 'contains': ['192.e1.a1', '288.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9245, 6843, 671, 3358, 9177, 4948, 739, 3770], 'generators': [96, 576, 384], 'label': '1152.155815.96.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['288.b1.a1', '384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '1152.155815', 'quotient_action_image': '12.4', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974158
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '96.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '24.c1.a1', 'complements': ['12.cg1.a1', '12.cj1.a1', '12.ch1.a1', '12.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.b1.a1', '48.cp1.a1', '48.cs1.a1', '48.cu1.a1', '48.cw1.a1'], 'contains': ['288.b1.a1', '384.b1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9766, 7622, 103, 2531, 9446, 5665, 252, 3070], 'generators': [32, 96, 576], 'label': '1152.155815.96.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1'], 'normal_contains': ['288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '1152.155815', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974159
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.o1.a1', '48.p1.a1', '48.q1.a1', '48.r1.a1', '48.s1.a1'], 'contains': ['192.a1.a1', '192.d1.a1', '192.e1.a1', '288.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5757, -1, 4272, -1, 5977, -1, 4058, -1], 'generators': [48, 96, 384], 'label': '1152.155815.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.d1.a1', 'projective_image': '576.8314', '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: 60974160
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '32.b1.a1', '48.u1.a1', '48.v1.a1', '48.w1.a1'], 'contains': ['192.b1.a1', '192.f1.a1', '288.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9606, -1, 591, -1, 9113, -1, 1969, -1], 'generators': [1, 48, 32], 'label': '1152.155815.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '96.e1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974161
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.c1.a1', '48.f1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1'], 'contains': ['192.a1.a1', '192.g1.a1', '288.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4796, -1, 5716, -1, 4120, -1, 3509, -1], 'generators': [1, 48, 384], 'label': '1152.155815.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.f1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974162
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.p1.a1', '24.bt1.a1', '24.bu1.a1', '24.bv1.a1', '32.e1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8695, 9379, 1165, 564, 8981, 7822, 1526, 498], 'generators': [3, 576, 96, 48, 32, 384], 'label': '1152.155815.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60974163
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.g1.a1', '48.x1.a1', '48.y1.a1', '48.ba1.a1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1'], 'contains': ['192.a1.a1', '192.h1.a1', '288.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3685, -1, 6126, -1, 4006, -1, 4182, -1], 'generators': [2, 48, 384], 'label': '1152.155815.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '96.g1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974164
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '32.c1.a1', '48.u1.a1', '48.v1.a1', '48.be1.a1'], 'contains': ['192.b1.a1', '192.i1.a1', '288.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9510, -1, 739, -1, 9064, -1, 1923, -1], 'generators': [2, 48, 32], 'label': '1152.155815.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '96.h1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974165
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.h1.a1', '48.bf1.a1', '48.bg1.a1', '48.bh1.a1', '48.bi1.a1', '48.bj1.a1', '48.bk1.a1'], 'contains': ['192.a1.a1', '192.j1.a1', '288.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1930, -1, 8928, -1, 2154, -1, 5691, -1], 'generators': [6, 48, 384], 'label': '1152.155815.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '96.i1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974166
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '32.d1.a1', '48.bl1.a1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.b1.a1', '192.k1.a1', '288.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8812, -1, 1242, -1, 7995, -1, 2299, -1], 'generators': [6, 48, 32], 'label': '1152.155815.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '96.j1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974167
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.i1.a1', '48.x1.a1', '48.ba1.a1', '48.bf1.a1', '48.bg1.a1', '48.bo1.a1', '48.bp1.a1'], 'contains': ['192.a1.a1', '192.l1.a1', '288.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3258, -1, 6651, -1, 3241, -1, 3791, -1], 'generators': [3, 48, 384], 'label': '1152.155815.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.k1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974168
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '32.e1.a1', '48.u1.a1', '48.bl1.a1', '48.bq1.a1'], 'contains': ['192.b1.a1', '192.m1.a1', '288.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9287, -1, 1020, -1, 8336, -1, 2015, -1], 'generators': [3, 48, 32], 'label': '1152.155815.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.l1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974169
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '32.e1.a1', '48.br1.a1'], 'contains': ['192.c1.a1', '192.n1.a1', '288.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7919, -1, 2732, -1, 7306, -1, 2415, -1], 'generators': [3, 48, 416], 'label': '1152.155815.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1.a1', 'old_label': '96.m1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974170
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.j1.a1', '48.z1.a1', '48.ba1.a1', '48.bb1.a1', '48.bs1.a1', '48.bt1.a1'], 'contains': ['192.a1.a1', '192.o1.a1', '288.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3525, -1, 6195, -1, 3821, -1, 4613, -1], 'generators': [97, 48, 384], 'label': '1152.155815.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '96.n1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974171
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.l1.a1', '48.z1.a1', '48.bd1.a1', '48.bk1.a1', '48.bp1.a1', '48.bt1.a1', '48.bx1.a1', '48.by1.a1', '48.bz1.a1'], 'contains': ['192.a1.a1', '288.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2418, -1, 6952, -1, 2725, -1, 6224, -1], 'generators': [168, 384, 48], 'label': '1152.155815.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.o1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974172
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.d1.a1', '48.m1.a1', '48.bf1.a1', '48.bh1.a1', '48.bx1.a1'], 'contains': ['192.a1.a1', '288.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3448, -1, 8229, -1, 2777, -1, 5834, -1], 'generators': [85, 48, 384], 'label': '1152.155815.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '96.p1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974173
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.e1.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.a1.a1', '24.b1.a1', '24.ca1.a1', '32.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6774, 5159, 3685, 3125, 7807, 6527, 3489, 4928], 'generators': [72, 576, 672, 32, 384, 48], 'label': '1152.155815.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.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.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60974174
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.p1.a1', '48.bg1.a1', '48.bi1.a1', '48.bu1.a1', '48.bx1.a1', '48.by1.a1'], 'contains': ['192.a1.a1', '288.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2661, -1, 7901, -1, 2100, -1, 6441, -1], 'generators': [181, 48, 384], 'label': '1152.155815.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '96.q1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974175
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '48.r1.a1', '48.y1.a1', '48.bb1.a1', '48.bh1.a1', '48.bi1.a1', '48.bo1.a1', '48.bp1.a1'], 'contains': ['192.a1.a1', '288.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3039, -1, 6758, -1, 2968, -1, 5296, -1], 'generators': [75, 48, 384], 'label': '1152.155815.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.r1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974176
    {'ambient': '1152.155815', 'aut_centralizer_order': 288, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '32.f1.a1', '48.w1.a1', '48.be1.a1', '48.bn1.a1', '48.bq1.a1', '48.ca1.a1', '48.cb1.a1', '48.cc1.a1'], 'contains': ['192.b1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7131, -1, 3014, -1, 7656, -1, 3697, -1], 'generators': [72, 32, 48], 'label': '1152.155815.96.s1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '96.s1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974177
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '96.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1.a1', '32.g1.a1', '48.bl1.a1', '48.bm1.a1', '48.ca1.a1'], 'contains': ['192.b1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8766, -1, 1286, -1, 7698, -1, 2488, -1], 'generators': [85, 32, 48], 'label': '1152.155815.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cw1.a1', 'old_label': '96.t1.a1', 'projective_image': '576.8314', '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': '4.2'}
  • id: 60974178
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '32.h1.a1', '48.v1.a1', '48.bm1.a1', '48.bq1.a1'], 'contains': ['192.b1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8845, -1, 1180, -1, 8233, -1, 2528, -1], 'generators': [75, 48, 32], 'label': '1152.155815.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.u1.a1', 'projective_image': '576.8314', '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': '12.4'}
  • id: 60974179
    {'ambient': '1152.155815', 'aut_centralizer_order': 144, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '32.f1.a1', '48.br1.a1', '48.cd1.a1', '48.ce1.a1'], 'contains': ['192.c1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4856, -1, 7145, -1, 5522, -1, 4517, -1], 'generators': [72, 416, 48], 'label': '1152.155815.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '96.v1.a1', 'projective_image': '576.8314', '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': '2.1'}
  • id: 60974180
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '32.h1.a1', '48.br1.a1'], 'contains': ['192.c1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7484, -1, 2836, -1, 7216, -1, 3863, -1], 'generators': [75, 48, 416], 'label': '1152.155815.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1.a1', 'old_label': '96.w1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974181
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.cf1.a1', '48.ch1.a1'], 'contains': ['192.d1.a1', '192.g1.a1', '192.o1.a1', '288.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7011, -1, 3230, -1, 7584, -1, 2367, -1], 'generators': [1, 144, 384], 'label': '1152.155815.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.x1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974182
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.cf1.a1', '48.cg1.a1'], 'contains': ['192.d1.a1', '192.h1.a1', '288.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6956, -1, 3270, -1, 7497, -1, 2579, -1], 'generators': [2, 144, 384], 'label': '1152.155815.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '96.y1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974183
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1'], 'contains': ['192.d1.a1', '192.j1.a1', '288.o1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5349, -1, 5139, -1, 5642, -1, 4567, -1], 'generators': [6, 720, 384], 'label': '1152.155815.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1.a1', 'old_label': '96.z1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974184
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.bx1.a1', '24.bz1.a1', '24.cb1.a1', '32.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8335, 8122, 2188, 1853, 8265, 9325, 2487, 1649], 'generators': [75, 576, 96, 48, 32, 384], 'label': '1152.155815.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60974185
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.cf1.a1'], 'contains': ['192.d1.a1', '192.l1.a1', '288.p1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6886, -1, 3374, -1, 7340, -1, 2447, -1], 'generators': [3, 144, 384], 'label': '1152.155815.96.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.ba1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974186
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.cg1.a1', '48.ch1.a1'], 'contains': ['192.d1.a1', '192.o1.a1', '288.q1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6914, -1, 3309, -1, 7447, -1, 2625, -1], 'generators': [577, 144, 384], 'label': '1152.155815.96.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bq1.a1', 'old_label': '96.bb1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974187
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.cg1.a1'], 'contains': ['192.d1.a1', '288.r1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6719, -1, 3515, -1, 6598, -1, 4008, -1], 'generators': [651, 144, 384], 'label': '1152.155815.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.bc1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974188
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.ch1.a1', '48.ci1.a1', '48.cj1.a1', '48.ck1.a1'], 'contains': ['192.d1.a1', '192.e1.a1', '288.s1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7825, -1, 2176, -1, 8485, -1, 1821, -1], 'generators': [624, 96, 384], 'label': '1152.155815.96.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bd1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974189
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.ch1.a1', '48.cl1.a1', '48.cl1.a2', '48.cm1.a1', '48.cm1.a2', '48.cq1.a1'], 'contains': ['192.e1.a1', '192.g1.a1', '192.o1.a1', '288.t1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8205, -1, 1752, -1, 8573, -1, 1389, -1], 'generators': [1, 96, 384], 'label': '1152.155815.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.be1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974190
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.ci1.a1', '48.cl1.a1', '48.cl1.a2', '48.cn1.a1', '48.cn1.a2', '48.cr1.a1'], 'contains': ['192.e1.a1', '192.h1.a1', '288.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8292, -1, 1965, -1, 8656, -1, 1343, -1], 'generators': [2, 96, 384], 'label': '1152.155815.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bf1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974191
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.cj1.a1', '48.ct1.a1'], 'contains': ['192.e1.a1', '192.j1.a1', '288.v1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7439, -1, 2666, -1, 6544, -1, 2193, -1], 'generators': [6, 672, 384], 'label': '1152.155815.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '96.bg1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974192
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.ck1.a1', '48.cl1.a1', '48.cl1.a2', '48.co1.a1', '48.co1.a2', '48.cv1.a1'], 'contains': ['192.e1.a1', '192.l1.a1', '288.w1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8177, -1, 1898, -1, 8607, -1, 1212, -1], 'generators': [3, 96, 384], 'label': '1152.155815.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '96.bh1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974193
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.ch1.a1', '48.cn1.a1', '48.cn1.a2', '48.co1.a1', '48.co1.a2', '48.cq1.a1'], 'contains': ['192.e1.a1', '192.o1.a1', '288.x1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8513, -1, 1925, -1, 8856, -1, 1280, -1], 'generators': [577, 96, 384], 'label': '1152.155815.96.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bi1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974194
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.ci1.a1', '48.cm1.a1', '48.cm1.a2', '48.co1.a1', '48.co1.a2', '48.cr1.a1'], 'contains': ['192.e1.a1', '288.y1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8641, -1, 1433, -1, 8927, -1, 941, -1], 'generators': [578, 384, 96], 'label': '1152.155815.96.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bj1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974195
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '24.bn1.a1', '24.bo1.a1', '32.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8918, -1, 1059, -1, 9136, -1, 1412, -1], 'generators': [1, 384, 576, 48, 32, 672], 'label': '1152.155815.8.d1.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.d1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60974196
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.cj1.a1', '48.ct1.a1'], 'contains': ['192.e1.a1', '288.z1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7520, -1, 2565, -1, 6674, -1, 1871, -1], 'generators': [582, 384, 672], 'label': '1152.155815.96.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '96.bk1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974197
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.ck1.a1', '48.cm1.a1', '48.cm1.a2', '48.cn1.a1', '48.cn1.a2', '48.cv1.a1'], 'contains': ['192.e1.a1', '288.ba1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8591, -1, 1482, -1, 8817, -1, 1076, -1], 'generators': [579, 96, 384], 'label': '1152.155815.96.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '96.bl1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974198
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.t1.a1', '48.cx1.a1'], 'contains': ['288.b1.a1', '384.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9122, -1, 1048, -1, 9333, -1, 577, -1], 'generators': [416, 96, 576], 'label': '1152.155815.96.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '96.bm1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60974199
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a1', '32.i1.a1', '48.u1.a1'], 'contains': ['192.f1.a1', '192.i1.a1', '192.m1.a1', '288.bb1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9698, -1, 302, -1, 9626, -1, 336, -1], 'generators': [1, 2, 32], 'label': '1152.155815.96.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1.a1', 'old_label': '96.bn1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974200
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a2', '32.i1.a2', '48.u1.a1'], 'contains': ['192.f1.a1', '192.i1.a1', '192.m1.a1', '288.bb1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9698, -1, 275, -1, 9626, -1, 368, -1], 'generators': [49, 2, 32], 'label': '1152.155815.96.bn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1.a1', 'old_label': '96.bn1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974201
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '48.x1.a1', '48.cf1.a1', '48.cl1.a1'], 'contains': ['192.g1.a1', '192.h1.a1', '192.l1.a1', '288.bb1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7357, -1, 2704, -1, 7735, -1, 1712, -1], 'generators': [1, 2, 384], 'label': '1152.155815.96.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '96.bo1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974202
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a2', '48.x1.a1', '48.cf1.a1', '48.cl1.a2'], 'contains': ['192.g1.a1', '192.h1.a1', '192.l1.a1', '288.bb1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7357, -1, 2316, -1, 7735, -1, 1744, -1], 'generators': [49, 2, 384], 'label': '1152.155815.96.bo1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '96.bo1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974203
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '48.cf1.a1', '48.cl1.a1'], 'contains': ['192.h1.a1', '192.l1.a1', '192.o1.a1', '288.bc1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7040, -1, 3188, -1, 7618, -1, 2115, -1], 'generators': [97, 2, 384], 'label': '1152.155815.96.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '96.bp1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974204
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '48.cf1.a1', '48.cl1.a2'], 'contains': ['192.h1.a1', '192.l1.a1', '192.o1.a1', '288.bc1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7040, -1, 3161, -1, 7618, -1, 2047, -1], 'generators': [145, 2, 384], 'label': '1152.155815.96.bp1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '96.bp1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974205
    {'ambient': '1152.155815', 'aut_centralizer_order': 288, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1'], 'contains': ['384.a1.a1', '384.b1.a1', '384.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9906, -1, 109, -1, 9353, -1, 556, -1], 'generators': [32, 384], 'label': '1152.155815.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '128.a1.a1', 'projective_image': '1152.155815', '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': '4.2'}
  • id: 60974206
    {'ambient': '1152.155815', 'aut_centralizer_order': 6, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1090146', 'aut_weyl_index': 6, 'centralizer': '192.a1.a1', 'complements': ['576.d1.a1', '576.h1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '6.b1.a1', '6.p1.a1', '8.k1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6659, 6144, 4518, 7651, 7540, 3081, 3415, 2625], 'generators': [2, 48, 32, 12, 72, 576, 96, 384], 'label': '1152.155815.2.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.f1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '576.8314', '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': '192.1472'}
  • id: 60974207
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '24.bp1.a1', '24.bq1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8986, -1, 993, -1, 9217, -1, 1311, -1], 'generators': [2, 576, 96, 48, 384, 32], 'label': '1152.155815.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '576.8314', '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': '96.226'}
  • id: 60974208
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '144.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.t1.a1', '72.a1.a1', '72.bl1.a1', '72.bm1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '72.bq1.a1'], 'contains': ['288.b1.a1', '288.c1.a1', '288.s1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7716, 5843, 2492, 4322, 7377, 4197, 2081, 4504], 'generators': [48, 96, 576], 'label': '1152.155815.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1'], 'normal_contains': ['288.b1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '6.1', 'quotient_action_kernel': '24.6', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974209
    {'ambient': '1152.155815', 'aut_centralizer_order': 1152, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.f1.a1', 'complements': ['8.o1.a1', '8.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.cb1.a1', '48.cd1.a1', '72.bc1.a1', '72.bu1.a1', '72.bw1.a1', '72.ch1.a1', '72.ck1.a1'], 'contains': ['288.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3556, 3681, 8070, 6491, 3275, 2281, 7959, 6133], 'generators': [12], 'label': '1152.155815.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.a1.a1', '48.e1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974210
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '72.bl1.a1'], 'contains': ['288.c1.a1', '288.d1.a1', '288.h1.a1', '288.m1.a1', '288.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6648, -1, 3612, -1, 6792, -1, 3383, -1], 'generators': [1, 48, 96], 'label': '1152.155815.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974211
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.b1.a1', '72.c1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '72.bm1.a1'], 'contains': ['288.c1.a1', '288.e1.a1', '288.n1.a1', '288.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6503, -1, 3807, -1, 6753, -1, 3933, -1], 'generators': [2, 48, 96], 'label': '1152.155815.144.d1.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': '144.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974212
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.bn1.a1'], 'contains': ['288.c1.a1', '288.f1.a1', '288.o1.a1', '288.v1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5237, -1, 4767, -1, 5021, -1, 4990, -1], 'generators': [6, 48, 672], 'label': '1152.155815.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '144.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974213
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.b1.a1', '72.l1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1', '72.u1.a1', '72.bo1.a1'], 'contains': ['288.c1.a1', '288.g1.a1', '288.p1.a1', '288.w1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5966, -1, 4092, -1, 6047, -1, 3172, -1], 'generators': [3, 48, 96], 'label': '1152.155815.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974214
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '72.f1.a1', '72.h1.a1', '72.i1.a1', '72.r1.a1', '72.v1.a1', '72.w1.a1', '72.bl1.a1'], 'contains': ['288.c1.a1', '288.h1.a1', '288.q1.a1', '288.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6461, -1, 3691, -1, 6715, -1, 3970, -1], 'generators': [577, 48, 96], 'label': '1152.155815.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.g1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974215
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '72.a1.a1', '72.g1.a1', '72.k1.a1', '72.q1.a1', '72.s1.a1', '72.w1.a1', '72.x1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1'], 'contains': ['288.a1.a1', '288.c1.a1', '288.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2726, -1, 6919, -1, 3427, -1, 6859, -1], 'generators': [72, 96], 'label': '1152.155815.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.h1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974216
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '72.a1.a1', '72.f1.a1', '72.j1.a1', '72.m1.a1', '72.t1.a1', '72.bg1.a1', '72.bh1.a1'], 'contains': ['288.c1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5682, -1, 4464, -1, 5707, -1, 4938, -1], 'generators': [648, 96], 'label': '1152.155815.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.i1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974217
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '72.l1.a1', '72.n1.a1', '72.x1.a1', '72.bg1.a1', '72.bi1.a1', '72.bj1.a1', '72.bp1.a1'], 'contains': ['288.c1.a1', '288.j1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5125, -1, 4874, -1, 4517, -1, 5783, -1], 'generators': [85, 96], 'label': '1152.155815.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '144.j1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974218
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.o1.a1', '24.br1.a1', '24.bs1.a1', '32.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8491, -1, 1635, -1, 8680, -1, 1598, -1], 'generators': [6, 576, 672, 48, 384, 32], 'label': '1152.155815.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.f1.a1', 'projective_image': '576.8314', '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': '96.226'}
  • id: 60974219
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '72.d1.a1', '72.e1.a1', '72.j1.a1', '72.r1.a1', '72.v1.a1', '72.y1.a1', '72.bm1.a1'], 'contains': ['288.c1.a1', '288.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6769, -1, 3466, -1, 7008, -1, 2684, -1], 'generators': [578, 48], 'label': '1152.155815.144.k1.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': '144.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974220
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.m1.a1', '72.u1.a1', '72.z1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bn1.a1'], 'contains': ['288.c1.a1', '288.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5552, -1, 4565, -1, 5210, -1, 3597, -1], 'generators': [582, 48], 'label': '1152.155815.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '144.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974221
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '72.o1.a1', '72.p1.a1', '72.u1.a1', '72.ba1.a1', '72.bg1.a1', '72.bk1.a1', '72.bp1.a1'], 'contains': ['288.c1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5021, -1, 4926, -1, 4871, -1, 5079, -1], 'generators': [661, 96], 'label': '1152.155815.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '144.m1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974222
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '72.d1.a1', '72.h1.a1', '72.o1.a1', '72.bb1.a1', '72.bh1.a1', '72.bi1.a1', '72.bo1.a1'], 'contains': ['288.c1.a1', '288.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5870, -1, 4196, -1, 6163, -1, 2963, -1], 'generators': [579, 48], 'label': '1152.155815.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.n1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974223
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '72.c1.a1', '72.n1.a1', '72.s1.a1', '72.v1.a1', '72.bh1.a1', '72.bk1.a1', '72.bq1.a1'], 'contains': ['288.c1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5736, -1, 4322, -1, 5470, -1, 4756, -1], 'generators': [75, 96], 'label': '1152.155815.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.o1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974224
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '72.e1.a1', '72.i1.a1', '72.p1.a1', '72.t1.a1', '72.bb1.a1', '72.bj1.a1', '72.bq1.a1'], 'contains': ['288.c1.a1', '288.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5922, -1, 4139, -1, 5874, -1, 4369, -1], 'generators': [651, 96], 'label': '1152.155815.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.p1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974225
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '48.x1.a1', '72.b1.a1', '72.br1.a1', '72.bs1.a1'], 'contains': ['288.d1.a1', '288.e1.a1', '288.g1.a1', '288.bb1.a1', '288.bb1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4922, -1, 5658, -1, 4569, -1, 3301, -1], 'generators': [1, 2, 48], 'label': '1152.155815.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.q1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974226
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '48.y1.a1', '72.c1.a1', '72.br1.a1', '72.bs1.a1'], 'contains': ['288.d1.a1', '288.e1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4833, -1, 5851, -1, 4065, -1, 4482, -1], 'generators': [73, 2], 'label': '1152.155815.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.r1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974227
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '72.f1.a1', '72.g1.a1', '72.br1.a1'], 'contains': ['288.d1.a1', '288.h1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3719, -1, 5984, -1, 3855, -1, 5460, -1], 'generators': [1, 168], 'label': '1152.155815.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.s1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974228
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.w1.a1', '72.g1.a1', '72.bs1.a1', '72.bt1.a1', '72.bu1.a1', '72.bv1.a1'], 'contains': ['288.a1.a1', '288.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3975, -1, 6240, -1, 3309, -1, 7112, -1], 'generators': [1, 72], 'label': '1152.155815.144.t1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.t1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974229
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.bw1.a1', '24.by1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8432, -1, 1744, -1, 8003, -1, 2335, -1], 'generators': [85, 384, 576, 32, 48, 672], 'label': '1152.155815.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.g1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60974230
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '72.b1.a1', '72.br1.a1', '72.by1.a1'], 'contains': ['288.e1.a1', '288.g1.a1', '288.h1.a1', '288.bc1.a1', '288.bc1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3511, -1, 5905, -1, 3945, -1, 3825, -1], 'generators': [97, 2, 48], 'label': '1152.155815.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.u1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974231
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '72.c1.a1', '72.br1.a1', '72.by1.a1'], 'contains': ['288.e1.a1', '288.h1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3480, -1, 6281, -1, 3787, -1, 5233, -1], 'generators': [169, 2], 'label': '1152.155815.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.v1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974250
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '72.ba1.a1', '72.bg1.a1', '72.cb1.a1'], 'contains': ['288.i1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2562, -1, 6678, -1, 3173, -1, 6981, -1], 'generators': [661, 168], 'label': '1152.155815.144.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '144.bn1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974232
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '48.be1.a1', '72.k1.a1', '72.bs1.a1', '72.bw1.a1', '72.bx1.a1', '72.by1.a1', '72.bz1.a1', '72.ca1.a1'], 'contains': ['288.a1.a1', '288.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1444, -1, 8432, -1, 3041, -1, 7222, -1], 'generators': [2, 72], 'label': '1152.155815.144.w1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.w1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974233
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1.a1', '72.k1.a1', '72.br1.a1', '72.cb1.a1'], 'contains': ['288.e1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3056, -1, 6550, -1, 3360, -1, 6259, -1], 'generators': [2, 168], 'label': '1152.155815.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.x1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974234
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1.a1', '48.bl1.a1', '72.l1.a1', '72.cc1.a1', '72.ce1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2980, -1, 8265, -1, 3007, -1, 5738, -1], 'generators': [85, 6], 'label': '1152.155815.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '144.y1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974235
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1.a1', '72.l1.a1', '72.cd1.a1', '72.ce1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1652, -1, 9332, -1, 2027, -1, 6404, -1], 'generators': [757, 6], 'label': '1152.155815.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '144.z1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974236
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '48.bm1.a1', '72.n1.a1', '72.cc1.a1', '72.ce1.a1'], 'contains': ['288.f1.a1', '288.j1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2939, -1, 8305, -1, 2850, -1, 5944, -1], 'generators': [61, 6], 'label': '1152.155815.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '144.ba1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974237
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.a1', '72.n1.a1', '72.cd1.a1', '72.ce1.a1'], 'contains': ['288.f1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1611, -1, 9372, -1, 1978, -1, 6491, -1], 'generators': [733, 6], 'label': '1152.155815.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '144.bb1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974238
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '48.bn1.a1', '72.q1.a1', '72.bt1.a1', '72.bw1.a1', '72.bx1.a1', '72.cc1.a1', '72.cd1.a1', '72.cf1.a1'], 'contains': ['288.a1.a1', '288.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1740, -1, 8735, -1, 2541, -1, 7498, -1], 'generators': [6, 72], 'label': '1152.155815.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.bc1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974239
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a1', '72.q1.a1', '72.ce1.a1', '72.cg1.a1'], 'contains': ['288.f1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1871, -1, 9241, -1, 2061, -1, 6934, -1], 'generators': [6, 744], 'label': '1152.155815.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '144.bd1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974240
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.i1.a1', '24.cc1.a1', '24.cg1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7964, -1, 2631, -1, 8377, -1, 3185, -1], 'generators': [1, 384, 32, 2, 72, 48], 'label': '1152.155815.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.h1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60974241
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '48.bq1.a1', '48.br1.a1', '72.s1.a1', '72.bs1.a1', '72.by1.a1', '72.cc1.a1', '72.cd1.a1', '72.ch1.a1', '72.ci1.a1'], 'contains': ['288.a1.a1', '288.g1.a1', '288.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2278, -1, 8472, -1, 3124, -1, 6799, -1], 'generators': [3, 72], 'label': '1152.155815.144.be1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.be1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974242
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.s1.a1', '72.br1.a1', '72.ce1.a1'], 'contains': ['288.g1.a1', '288.i1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1938, -1, 7034, -1, 2914, -1, 5884, -1], 'generators': [3, 168], 'label': '1152.155815.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bf1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974243
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.g1.a1', '72.w1.a1', '72.by1.a1', '72.cf1.a1', '72.cj1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1', '288.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1680, -1, 8344, -1, 2648, -1, 8193, -1], 'generators': [97, 72], 'label': '1152.155815.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bg1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974244
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.f1.a1', '72.w1.a1', '72.cg1.a1'], 'contains': ['288.h1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2361, -1, 7105, -1, 3207, -1, 6291, -1], 'generators': [577, 168], 'label': '1152.155815.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '144.bh1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974245
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.ca1.a1', '72.x1.a1', '72.bu1.a1', '72.bz1.a1', '72.cc1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '288.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2319, -1, 8404, -1, 3075, -1, 7447, -1], 'generators': [85, 72], 'label': '1152.155815.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.bi1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974246
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '72.x1.a1', '72.ba1.a1', '72.bv1.a1', '72.ca1.a1', '72.cd1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1', '288.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2061, -1, 7866, -1, 2347, -1, 8374, -1], 'generators': [181, 72], 'label': '1152.155815.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bj1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60974247
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '72.bc1.a1', '72.bd1.a1', '72.bv1.a1', '72.bx1.a1', '72.ci1.a1', '72.cj1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1362, -1, 8634, -1, 2245, -1, 9232, -1], 'generators': [108], 'label': '1152.155815.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.bk1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974248
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '48.cc1.a1', '48.ce1.a1', '72.bf1.a1', '72.bt1.a1', '72.bz1.a1', '72.ca1.a1', '72.cf1.a1', '72.ch1.a1', '72.ci1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1390, -1, 9047, -1, 2682, -1, 8100, -1], 'generators': [7], 'label': '1152.155815.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bl1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974249
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.x1.a1', '72.bg1.a1', '72.ce1.a1'], 'contains': ['288.i1.a1', '288.j1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3407, -1, 7606, -1, 2614, -1, 6537, -1], 'generators': [85, 168], 'label': '1152.155815.144.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '144.bm1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974251
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.l1.a1', '24.cd1.a1', '24.ch1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5393, -1, 5093, -1, 7268, -1, 4062, -1], 'generators': [1, 384, 32, 6, 72, 48], 'label': '1152.155815.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.i1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60974252
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1.a1', '72.be1.a1', '72.cb1.a1', '72.cg1.a1'], 'contains': ['288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2406, -1, 6724, -1, 2580, -1, 7382, -1], 'generators': [103], 'label': '1152.155815.144.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.bo1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974253
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.a1', '72.b1.a1'], 'contains': ['288.m1.a1', '288.n1.a1', '288.p1.a1', '288.bb1.a1', '288.bb1.a2', '288.bc1.a1', '288.bc1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7053, -1, 3160, -1, 7548, -1, 2333, -1], 'generators': [1, 2, 144], 'label': '1152.155815.144.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '144.bp1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974254
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1.a1', '72.i1.a1'], 'contains': ['288.n1.a1', '288.q1.a1', '288.r1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6865, -1, 3250, -1, 7254, -1, 3899, -1], 'generators': [649, 2], 'label': '1152.155815.144.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1.a1', 'old_label': '144.bq1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974255
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1.a1', '72.bl1.a1', '72.cm1.a1', '72.cm1.a2'], 'contains': ['288.m1.a1', '288.q1.a1', '288.s1.a1', '288.t1.a1', '288.x1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8087, -1, 2206, -1, 8537, -1, 1427, -1], 'generators': [1, 624, 96], 'label': '1152.155815.144.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.br1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974256
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1.a1', '72.bm1.a1', '72.cm1.a1', '72.cm1.a2'], 'contains': ['288.s1.a1', '288.u1.a1', '288.y1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8462, -1, 2085, -1, 8778, -1, 1144, -1], 'generators': [2, 624], 'label': '1152.155815.144.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '144.bs1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974257
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1.a1', '72.bn1.a1'], 'contains': ['288.s1.a1', '288.v1.a1', '288.z1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7379, -1, 2630, -1, 6637, -1, 2147, -1], 'generators': [6, 624], 'label': '1152.155815.144.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '144.bt1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974258
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1.a1', '72.bo1.a1', '72.cm1.a1', '72.cm1.a2'], 'contains': ['288.s1.a1', '288.w1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8117, -1, 1846, -1, 8744, -1, 1112, -1], 'generators': [3, 624], 'label': '1152.155815.144.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bu1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974259
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1.a1', '72.b1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.t1.a1', '288.u1.a1', '288.w1.a1', '288.bb1.a1', '288.bc1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8388, -1, 2175, -1, 8708, -1, 1246, -1], 'generators': [1, 2, 96], 'label': '1152.155815.144.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bv1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974260
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1.a2', '72.b1.a1', '72.cm1.a2', '72.cn1.a2'], 'contains': ['288.t1.a1', '288.u1.a1', '288.w1.a1', '288.bb1.a2', '288.bc1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8388, -1, 1643, -1, 8708, -1, 1178, -1], 'generators': [49, 2, 96], 'label': '1152.155815.144.bv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bv1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974261
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.a1', '72.d1.a1', '72.cm1.a1', '72.cn1.a2'], 'contains': ['288.t1.a1', '288.y1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8646, -1, 1518, -1, 8981, -1, 859, -1], 'generators': [49, 578], 'label': '1152.155815.144.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bw1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974262
    {'ambient': '1152.155815', 'aut_centralizer_order': 6, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.j1.a1', '16.k1.a1', '24.c1.a1', '24.ce1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5271, -1, 5189, -1, 6735, -1, 3786, -1], 'generators': [1, 384, 48, 12, 32, 24], 'label': '1152.155815.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.j1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974263
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.a2', '72.d1.a1', '72.cm1.a2', '72.cn1.a1'], 'contains': ['288.t1.a1', '288.y1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8646, -1, 1432, -1, 8981, -1, 799, -1], 'generators': [1, 578], 'label': '1152.155815.144.bw1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bw1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974264
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '72.h1.a1', '72.cm1.a1', '72.cn1.a2'], 'contains': ['288.u1.a1', '288.x1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8520, -1, 1874, -1, 8890, -1, 1040, -1], 'generators': [625, 2], 'label': '1152.155815.144.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bx1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974265
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a2', '72.h1.a1', '72.cm1.a2', '72.cn1.a1'], 'contains': ['288.u1.a1', '288.x1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8520, -1, 1585, -1, 8890, -1, 1008, -1], 'generators': [577, 2], 'label': '1152.155815.144.bx1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bx1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974266
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.r1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.w1.a1', '288.x1.a1', '288.y1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8606, -1, 2058, -1, 9030, -1, 976, -1], 'generators': [577, 578], 'label': '1152.155815.144.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.by1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974267
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a2', '72.r1.a1', '72.cm1.a2', '72.cn1.a2'], 'contains': ['288.w1.a1', '288.x1.a1', '288.y1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8606, -1, 1558, -1, 9030, -1, 905, -1], 'generators': [625, 578], 'label': '1152.155815.144.by1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.by1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974268
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1.a1', '48.cq1.a1', '72.bl1.a1', '72.cn1.a1', '72.cn1.a2'], 'contains': ['288.b1.a1', '288.t1.a1', '288.x1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9360, -1, 574, -1, 9263, -1, 691, -1], 'generators': [1, 96, 576], 'label': '1152.155815.144.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '144.bz1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974269
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cr1.a1', '48.cs1.a1', '72.bm1.a1', '72.cn1.a1', '72.cn1.a2'], 'contains': ['288.b1.a1', '288.u1.a1', '288.y1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9487, -1, 426, -1, 9299, -1, 657, -1], 'generators': [2, 576], 'label': '1152.155815.144.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '144.ca1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974270
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ct1.a1', '48.cu1.a1', '72.bn1.a1'], 'contains': ['288.b1.a1', '288.v1.a1', '288.z1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8418, -1, 1378, -1, 7413, -1, 1776, -1], 'generators': [6, 576], 'label': '1152.155815.144.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '144.cb1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974271
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cv1.a1', '48.cw1.a1', '48.cx1.a1', '72.bo1.a1', '72.cn1.a1', '72.cn1.a2'], 'contains': ['288.b1.a1', '288.w1.a1', '288.ba1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9391, -1, 509, -1, 9226, -1, 625, -1], 'generators': [3, 576], 'label': '1152.155815.144.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.cc1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60974272
    {'ambient': '1152.155815', 'aut_centralizer_order': 2304, 'aut_label': '192.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.d1.a1', '96.f1.a1', '96.g1.a1', '96.i1.a1', '96.k1.a1', '96.n1.a1', '96.o1.a1', '96.p1.a1', '96.q1.a1', '96.r1.a1'], 'contains': ['384.a1.a1', '576.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3332, 5328, 6636, 4895, 3233, 3790, 4579, 4894], 'generators': [48, 384], 'label': '1152.155815.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.a1.a1', '96.a1.a1'], 'normal_contains': ['384.a1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.187', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974273
    {'ambient': '1152.155815', 'aut_centralizer_order': 6, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.l1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.k1.a1', '24.cj1.a1', '24.cp1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6839, -1, 4518, -1, 7597, -1, 3383, -1], 'generators': [2, 32, 48, 12, 384, 72], 'label': '1152.155815.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.k1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974274
    {'ambient': '1152.155815', 'aut_centralizer_order': 576, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '64.a1.a1', '96.e1.a1', '96.h1.a1', '96.j1.a1', '96.l1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1'], 'contains': ['384.b1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9197, -1, 1016, -1, 8287, -1, 2014, -1], 'generators': [48, 32], 'label': '1152.155815.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '192.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974275
    {'ambient': '1152.155815', 'aut_centralizer_order': 288, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '64.a1.a1', '96.m1.a1', '96.v1.a1', '96.w1.a1'], 'contains': ['384.c1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7503, -1, 2853, -1, 7281, -1, 2430, -1], 'generators': [48, 416], 'label': '1152.155815.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '192.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974276
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.x1.a1', '96.y1.a1', '96.z1.a1', '96.ba1.a1', '96.bb1.a1', '96.bc1.a1', '96.bd1.a1'], 'contains': ['384.a1.a1', '576.b1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6961, -1, 3317, -1, 7383, -1, 2549, -1], 'generators': [144, 384], 'label': '1152.155815.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.d1.a1', 'projective_image': '1152.155815', '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': '2.1'}
  • id: 60974277
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.d1.a1', '96.bd1.a1', '96.be1.a1', '96.bf1.a1', '96.bg1.a1', '96.bh1.a1', '96.bi1.a1', '96.bj1.a1', '96.bk1.a1', '96.bl1.a1'], 'contains': ['384.a1.a1', '576.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8191, -1, 1979, -1, 8573, -1, 1343, -1], 'generators': [96, 384], 'label': '1152.155815.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.e1.a1', 'projective_image': '1152.155815', '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': '2.1'}
  • id: 60974278
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1.a1', '64.b1.a1', '96.e1.a1', '96.bn1.a1', '96.bn1.a2'], 'contains': ['384.b1.a1', '576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9825, -1, 211, -1, 9535, -1, 431, -1], 'generators': [1, 32], 'label': '1152.155815.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1.a1', 'old_label': '192.f1.a1', 'projective_image': '1152.155815', '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': '2.1'}
  • id: 60974279
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.f1.a1', '96.x1.a1', '96.be1.a1', '96.bo1.a1', '96.bo1.a2'], 'contains': ['384.a1.a1', '576.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7428, -1, 2597, -1, 7725, -1, 1886, -1], 'generators': [1, 384], 'label': '1152.155815.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '192.g1.a1', 'projective_image': '1152.155815', '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': '6.1'}
  • id: 60974280
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.g1.a1', '96.y1.a1', '96.bf1.a1', '96.bo1.a1', '96.bo1.a2', '96.bp1.a1', '96.bp1.a2'], 'contains': ['384.a1.a1', '576.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7306, -1, 2826, -1, 7691, -1, 1950, -1], 'generators': [2, 384], 'label': '1152.155815.192.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '192.h1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974281
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cs1.a1', '64.c1.a1', '96.h1.a1', '96.bn1.a1', '96.bn1.a2'], 'contains': ['384.b1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9766, -1, 297, -1, 9476, -1, 522, -1], 'generators': [2, 32], 'label': '1152.155815.192.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '192.i1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974282
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '96.i1.a1', '96.z1.a1', '96.bg1.a1'], 'contains': ['384.a1.a1', '576.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6589, -1, 3133, -1, 6554, -1, 2581, -1], 'generators': [6, 384], 'label': '1152.155815.192.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.p1.a1', 'old_label': '192.j1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974283
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '96.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cu1.a1', '64.d1.a1', '96.j1.a1'], 'contains': ['384.b1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9367, -1, 770, -1, 8380, -1, 1571, -1], 'generators': [6, 32], 'label': '1152.155815.192.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '192.k1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974284
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.l1.a1'], 'contains': ['16.e1.a1', '16.j1.a1', '16.l1.a1', '24.cm1.a1', '24.cq1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6909, -1, 4892, -1, 6667, -1, 3723, -1], 'generators': [85, 384, 32, 2, 72, 48], 'label': '1152.155815.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.l1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60974285
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '96.k1.a1', '96.ba1.a1', '96.bh1.a1', '96.bo1.a1', '96.bo1.a2', '96.bp1.a1', '96.bp1.a2'], 'contains': ['384.a1.a1', '576.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7277, -1, 2794, -1, 7657, -1, 1918, -1], 'generators': [3, 384], 'label': '1152.155815.192.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '192.l1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974286
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cw1.a1', '64.e1.a1', '96.l1.a1', '96.bn1.a1', '96.bn1.a2'], 'contains': ['384.b1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9957, -1, 255, -1, 9390, -1, 481, -1], 'generators': [3, 32], 'label': '1152.155815.192.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '192.m1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974288
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '96.x1.a1', '96.bb1.a1', '96.be1.a1', '96.bi1.a1', '96.bp1.a1', '96.bp1.a2'], 'contains': ['384.a1.a1', '576.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7249, -1, 3033, -1, 7584, -1, 2118, -1], 'generators': [97, 384], 'label': '1152.155815.192.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '192.o1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974289
    {'ambient': '1152.155815', 'aut_centralizer_order': 2304, 'aut_label': '288.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.s1.a1', '96.v1.a1', '144.b1.a1', '144.h1.a1', '144.t1.a1', '144.w1.a1', '144.bc1.a1', '144.be1.a1', '144.bg1.a1', '144.bi1.a1', '144.bj1.a1', '144.bk1.a1', '144.bl1.a1'], 'contains': ['576.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2278, 4365, 8326, 5835, 3075, 3101, 7347, 5870], 'generators': [72], 'label': '1152.155815.288.a1.a1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.a1.a1', '144.b1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.189', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974290
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '288.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.a1.a1', 'complements': ['4.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.c1.a1', '96.bm1.a1', '144.a1.a1', '144.bz1.a1', '144.ca1.a1', '144.cb1.a1', '144.cc1.a1'], 'contains': ['576.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9479, 6843, 481, 3358, 9226, 4928, 691, 3797], 'generators': [96, 576], 'label': '1152.155815.288.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['96.b1.a1', '96.c1.a1', '144.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '1152.155815', 'quotient_action_image': '6.1', 'quotient_action_kernel': '48.6', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60974291
    {'ambient': '1152.155815', 'aut_centralizer_order': 1536, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '144.a1.a1', '144.c1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1', '144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '144.o1.a1', '144.p1.a1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5870, -1, 4196, -1, 5977, -1, 3970, -1], 'generators': [48, 96], 'label': '1152.155815.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974292
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.f1.a1', '144.c1.a1', '144.q1.a1', '144.r1.a1', '144.s1.a1', '144.t1.a1'], 'contains': ['576.a1.a1', '576.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4899, -1, 5713, -1, 4120, -1, 3509, -1], 'generators': [1, 48], 'label': '1152.155815.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '288.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974293
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.h1.a1', '144.d1.a1', '144.q1.a1', '144.r1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1', '144.x1.a1'], 'contains': ['576.a1.a1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3698, -1, 5876, -1, 4006, -1, 4182, -1], 'generators': [2, 48], 'label': '1152.155815.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '288.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974294
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.j1.a1', '144.e1.a1', '144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1', '144.bc1.a1', '144.bd1.a1'], 'contains': ['576.a1.a1', '576.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2622, -1, 8471, -1, 2850, -1, 5738, -1], 'generators': [6, 48], 'label': '1152.155815.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '288.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974295
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.l1.a1'], 'contains': ['16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '24.cr1.a1', '24.cw1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7607, -1, 3472, -1, 7447, -1, 3236, -1], 'generators': [85, 384, 32, 6, 72, 48], 'label': '1152.155815.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.m1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60974296
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.l1.a1', '96.m1.a1', '144.f1.a1', '144.q1.a1', '144.u1.a1', '144.y1.a1', '144.z1.a1', '144.be1.a1', '144.bf1.a1'], 'contains': ['576.a1.a1', '576.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3463, -1, 6065, -1, 3820, -1, 3808, -1], 'generators': [3, 48], 'label': '1152.155815.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.g1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974297
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '144.c1.a1', '144.g1.a1', '144.s1.a1', '144.u1.a1', '144.v1.a1', '144.bg1.a1', '144.bh1.a1'], 'contains': ['576.a1.a1', '576.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3511, -1, 5970, -1, 3858, -1, 4613, -1], 'generators': [97, 48], 'label': '1152.155815.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '288.h1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974298
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1.a1', '144.h1.a1', '144.i1.a1', '144.s1.a1', '144.x1.a1', '144.bd1.a1', '144.bf1.a1', '144.bh1.a1', '144.bm1.a1', '144.bn1.a1', '144.bo1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2704, -1, 6818, -1, 3190, -1, 6275, -1], 'generators': [168], 'label': '1152.155815.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.i1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974299
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.t1.a1', '144.j1.a1', '144.y1.a1', '144.ba1.a1', '144.bi1.a1', '144.bm1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3414, -1, 7936, -1, 3267, -1, 5808, -1], 'generators': [85], 'label': '1152.155815.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '288.j1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974300
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.a1', '144.j1.a1', '144.m1.a1', '144.z1.a1', '144.bb1.a1', '144.bj1.a1', '144.bm1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2652, -1, 7606, -1, 2614, -1, 6441, -1], 'generators': [181], 'label': '1152.155815.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '288.k1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974301
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '96.u1.a1', '96.w1.a1', '144.o1.a1', '144.r1.a1', '144.v1.a1', '144.ba1.a1', '144.bb1.a1', '144.be1.a1', '144.bf1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3386, -1, 6281, -1, 3783, -1, 5233, -1], 'generators': [75], 'label': '1152.155815.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.l1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974302
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.x1.a1', '144.c1.a1', '144.bp1.a1', '144.br1.a1'], 'contains': ['576.b1.a1', '576.d1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7134, -1, 3152, -1, 7548, -1, 2333, -1], 'generators': [1, 144], 'label': '1152.155815.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.m1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974303
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1.a1', '144.d1.a1', '144.bp1.a1', '144.bq1.a1'], 'contains': ['576.b1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6994, -1, 3198, -1, 7497, -1, 2479, -1], 'generators': [2, 144], 'label': '1152.155815.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '288.n1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974305
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ba1.a1', '144.f1.a1', '144.bp1.a1'], 'contains': ['576.b1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6905, -1, 3276, -1, 7419, -1, 2396, -1], 'generators': [3, 144], 'label': '1152.155815.288.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '288.p1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974306
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.l1.a1'], 'contains': ['16.i1.a1', '16.k1.a1', '16.l1.a1', '24.cx1.a1', '24.cz1.a1', '24.da1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4983, -1, 5688, -1, 6316, -1, 5567, -1], 'generators': [3, 384, 32, 12, 24, 48], 'label': '1152.155815.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.n1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60974307
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '144.g1.a1', '144.bq1.a1', '144.br1.a1'], 'contains': ['576.b1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6938, -1, 3230, -1, 7458, -1, 2515, -1], 'generators': [577, 144], 'label': '1152.155815.288.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1.a1', 'old_label': '288.q1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974308
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1.a1', '144.p1.a1', '144.bq1.a1'], 'contains': ['576.b1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6738, -1, 3305, -1, 6599, -1, 3917, -1], 'generators': [651], 'label': '1152.155815.288.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '288.r1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974309
    {'ambient': '1152.155815', 'aut_centralizer_order': 768, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bd1.a1', '144.a1.a1', '144.br1.a1', '144.bs1.a1', '144.bt1.a1', '144.bu1.a1'], 'contains': ['576.b1.a1', '576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7961, -1, 2215, -1, 8511, -1, 1481, -1], 'generators': [624, 96], 'label': '1152.155815.288.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.s1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974310
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.be1.a1', '144.c1.a1', '144.br1.a1', '144.bv1.a1', '144.bv1.a2', '144.bw1.a1', '144.bw1.a2', '144.bz1.a1'], 'contains': ['576.c1.a1', '576.d1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8336, -1, 1853, -1, 8609, -1, 1297, -1], 'generators': [1, 96], 'label': '1152.155815.288.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.t1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974311
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bf1.a1', '144.d1.a1', '144.bs1.a1', '144.bv1.a1', '144.bv1.a2', '144.bx1.a1', '144.bx1.a2', '144.ca1.a1'], 'contains': ['576.c1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8426, -1, 1947, -1, 8703, -1, 1248, -1], 'generators': [2, 96], 'label': '1152.155815.288.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.u1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974312
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1.a1', '144.e1.a1', '144.bt1.a1', '144.cb1.a1'], 'contains': ['576.c1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7346, -1, 2694, -1, 6636, -1, 2172, -1], 'generators': [6, 672], 'label': '1152.155815.288.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '288.v1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974313
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1.a1', '144.f1.a1', '144.bu1.a1', '144.bv1.a1', '144.bv1.a2', '144.by1.a1', '144.by1.a2', '144.cc1.a1'], 'contains': ['576.c1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8368, -1, 1885, -1, 8659, -1, 1176, -1], 'generators': [3, 96], 'label': '1152.155815.288.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '288.w1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974314
    {'ambient': '1152.155815', 'aut_centralizer_order': 64, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bi1.a1', '144.g1.a1', '144.br1.a1', '144.bx1.a1', '144.bx1.a2', '144.by1.a1', '144.by1.a2', '144.bz1.a1'], 'contains': ['576.c1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8458, -1, 1916, -1, 8854, -1, 1212, -1], 'generators': [577, 96], 'label': '1152.155815.288.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.x1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974315
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bj1.a1', '144.k1.a1', '144.bs1.a1', '144.bw1.a1', '144.bw1.a2', '144.by1.a1', '144.by1.a2', '144.ca1.a1'], 'contains': ['576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8516, -1, 1573, -1, 8927, -1, 941, -1], 'generators': [578], 'label': '1152.155815.288.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.y1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974316
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1.a1', '144.l1.a1', '144.bt1.a1', '144.cb1.a1'], 'contains': ['576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7376, -1, 2666, -1, 6674, -1, 1982, -1], 'generators': [582], 'label': '1152.155815.288.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '288.z1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974317
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.f1.a1', '576.d1.a1', '576.h1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.q1.a1', '6.r1.a1', '8.l1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6780, 2879, 4795, 3946, 7101, 4266, 3745, 6940], 'generators': [85, 32, 384, 2, 48, 576, 96, 72], 'label': '1152.155815.2.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.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60974318
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.m1.a1', '16.n1.a1', '16.p1.a1', '24.df1.a1', '24.dg1.a1', '32.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9606, -1, 442, -1, 9845, -1, 267, -1], 'generators': [1, 576, 96, 2, 32, 384], 'label': '1152.155815.8.o1.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': '8.o1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60974319
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bl1.a1', '144.n1.a1', '144.bu1.a1', '144.bw1.a1', '144.bw1.a2', '144.bx1.a1', '144.bx1.a2', '144.cc1.a1'], 'contains': ['576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8488, -1, 1546, -1, 8817, -1, 1040, -1], 'generators': [579], 'label': '1152.155815.288.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '288.ba1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974320
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1.a1', '96.bo1.a1', '144.q1.a1', '144.bp1.a1', '144.bv1.a1'], 'contains': ['576.d1.a1', '576.e1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7451, -1, 2750, -1, 7762, -1, 1816, -1], 'generators': [1, 2], 'label': '1152.155815.288.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.bb1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974321
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1.a2', '96.bo1.a2', '144.q1.a1', '144.bp1.a1', '144.bv1.a2'], 'contains': ['576.d1.a1', '576.e1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7451, -1, 2622, -1, 7762, -1, 1852, -1], 'generators': [49, 2], 'label': '1152.155815.288.bb1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.bb1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974322
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bp1.a1', '144.u1.a1', '144.bp1.a1', '144.bv1.a1'], 'contains': ['576.e1.a1', '576.g1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7172, -1, 2969, -1, 7621, -1, 2084, -1], 'generators': [97, 2], 'label': '1152.155815.288.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.bc1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974323
    {'ambient': '1152.155815', 'aut_centralizer_order': 32, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bp1.a2', '144.u1.a1', '144.bp1.a1', '144.bv1.a2'], 'contains': ['576.e1.a1', '576.g1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7172, -1, 2922, -1, 7621, -1, 2048, -1], 'generators': [145, 2], 'label': '1152.155815.288.bc1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.bc1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974324
    {'ambient': '1152.155815', 'aut_centralizer_order': 2304, 'aut_label': '384.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.a1.a1', '192.d1.a1', '192.e1.a1', '192.g1.a1', '192.h1.a1', '192.j1.a1', '192.l1.a1', '192.o1.a1'], 'contains': ['1152.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7285, 6328, 2847, 3893, 7623, 4390, 1966, 4281], 'generators': [384], 'label': '1152.155815.384.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.b1.a1', '192.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '1152.155815', 'quotient_action_image': '2.1', 'quotient_action_kernel': '192.961', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974325
    {'ambient': '1152.155815', 'aut_centralizer_order': 576, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '128.a1.a1', '192.b1.a1', '192.f1.a1', '192.i1.a1', '192.k1.a1', '192.m1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9847, -1, 255, -1, 9371, -1, 540, -1], 'generators': [32], 'label': '1152.155815.384.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '384.b1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974326
    {'ambient': '1152.155815', 'aut_centralizer_order': 288, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bm1.a1', '128.a1.a1', '192.c1.a1', '192.n1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8879, -1, 1274, -1, 9272, -1, 637, -1], 'generators': [416], 'label': '1152.155815.384.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '384.c1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60974327
    {'ambient': '1152.155815', 'aut_centralizer_order': 4608, 'aut_label': '576.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '288.a1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.f1.a1', '288.g1.a1', '288.h1.a1', '288.i1.a1', '288.j1.a1', '288.k1.a1', '288.l1.a1'], 'contains': ['1152.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3463, 5563, 6065, 4608, 3820, 3859, 4579, 4854], 'generators': [48], 'label': '1152.155815.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['144.a1.a1', '192.a1.a1', '288.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': '1.1', 'quotient_action_kernel': '576.8314', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974328
    {'ambient': '1152.155815', 'aut_centralizer_order': 1536, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.d1.a1', '288.c1.a1', '288.m1.a1', '288.n1.a1', '288.o1.a1', '288.p1.a1', '288.q1.a1', '288.r1.a1', '288.s1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6952, -1, 3240, -1, 7438, -1, 2496, -1], 'generators': [144], 'label': '1152.155815.576.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '576.b1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974329
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.m1.a1', '16.n1.a1', '16.p1.a1', '24.df1.a2', '24.dg1.a2', '32.i1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9606, -1, 281, -1, 9845, -1, 326, -1], 'generators': [49, 576, 96, 2, 32, 384], 'label': '1152.155815.8.o1.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': '8.o1.a2', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a2', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60974330
    {'ambient': '1152.155815', 'aut_centralizer_order': 1536, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.e1.a1', '288.b1.a1', '288.c1.a1', '288.s1.a1', '288.t1.a1', '288.u1.a1', '288.v1.a1', '288.w1.a1', '288.x1.a1', '288.y1.a1', '288.z1.a1', '288.ba1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8336, -1, 1947, -1, 8609, -1, 1297, -1], 'generators': [96], 'label': '1152.155815.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '576.c1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974331
    {'ambient': '1152.155815', 'aut_centralizer_order': 384, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.f1.a1', '192.g1.a1', '288.d1.a1', '288.m1.a1', '288.t1.a1', '288.bb1.a1', '288.bb1.a2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7367, -1, 2674, -1, 7725, -1, 1870, -1], 'generators': [1], 'label': '1152.155815.576.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '576.d1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974332
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.h1.a1', '192.i1.a1', '288.e1.a1', '288.n1.a1', '288.u1.a1', '288.bb1.a1', '288.bb1.a2', '288.bc1.a1', '288.bc1.a2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7322, -1, 2826, -1, 7691, -1, 1934, -1], 'generators': [2], 'label': '1152.155815.576.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '576.e1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974333
    {'ambient': '1152.155815', 'aut_centralizer_order': 192, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.j1.a1', '192.k1.a1', '288.f1.a1', '288.o1.a1', '288.v1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6772, -1, 3048, -1, 6601, -1, 2563, -1], 'generators': [6], 'label': '1152.155815.576.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.p1.a1', 'old_label': '576.f1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974334
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.l1.a1', '192.m1.a1', '192.n1.a1', '288.g1.a1', '288.p1.a1', '288.w1.a1', '288.bb1.a1', '288.bb1.a2', '288.bc1.a1', '288.bc1.a2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7426, -1, 2783, -1, 7657, -1, 1902, -1], 'generators': [3], 'label': '1152.155815.576.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '576.g1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974335
    {'ambient': '1152.155815', 'aut_centralizer_order': 128, 'aut_label': '576.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.o1.a1', '288.h1.a1', '288.m1.a1', '288.q1.a1', '288.t1.a1', '288.x1.a1', '288.bc1.a1', '288.bc1.a2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7210, -1, 3009, -1, 7587, -1, 2084, -1], 'generators': [97], 'label': '1152.155815.576.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '576.h1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974336
    {'ambient': '1152.155815', 'aut_centralizer_order': None, 'aut_label': '1152.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': ['384.a1.a1', '384.b1.a1', '384.c1.a1', '576.a1.a1', '576.b1.a1', '576.c1.a1', '576.d1.a1', '576.e1.a1', '576.f1.a1', '576.g1.a1', '576.h1.a1'], 'contains': [], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7322, 6328, 2826, 3893, 7657, 4390, 1934, 4281], 'generators': [], 'label': '1152.155815.1152.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1152.a1.a1', 'normal_contained_in': ['288.b1.a1', '384.a1.a1', '576.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1152.a1.a1', 'projective_image': '1152.155815', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60974337
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '18.n1.a1', '18.o1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3675, -1, 6603, -1, 4034, -1, 7355, -1], 'generators': [1, 2, 12, 576], 'label': '1152.155815.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60974338
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.958', 'aut_weyl_index': 16, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.i1.a1', '24.y1.a1', '24.bo1.a1', '36.bj1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4501, 3828, 5619, 8050, 5447, 3143, 5674, 7338], 'generators': [1, 384, 48, 72, 96, 576], 'label': '1152.155815.12.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.a1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '576.8314', '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': '144.145'}
  • id: 60974339
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '192.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.k1.a1', '6.r1.a1'], 'contains': ['24.b1.a1', '24.bq1.a1', '36.bk1.a1', '48.be1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6966, 6681, 3370, 4571, 8507, 5024, 2877, 3164], 'generators': [2, 576, 96, 72, 48, 32], 'label': '1152.155815.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '576.8314', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60974340
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '192.a1.a1', 'complements': ['96.bo1.a1', '96.bp1.a1', '96.bo1.a2', '96.bp1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.l1.a1', '6.t1.a1'], 'contains': ['24.b1.a1', '24.bs1.a1', '36.bn1.a1', '48.bn1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6885, 7350, 3336, 3885, 7747, 5651, 3003, 2551], 'generators': [6, 576, 672, 72, 48, 32], 'label': '1152.155815.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 60974341
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.958', 'aut_weyl_index': 16, 'centralizer': '144.a1.a1', 'complements': ['96.bn1.a1', '96.bn1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.q1.a1', '6.s1.a1'], 'contains': ['24.a1.a1', '24.z1.a1', '24.bc1.a1', '24.bi1.a1', '24.bw1.a1', '36.bp1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4574, 2452, 5330, 6642, 4799, 1854, 6347, 8596], 'generators': [85, 384, 48, 72, 96, 576], 'label': '1152.155815.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.145'}
  • id: 60974342
    {'ambient': '1152.155815', 'aut_centralizer_order': 96, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '12.e1.a1', 'complements': ['96.bn1.a1', '96.bn1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.p1.a1', '6.u1.a1'], 'contains': ['24.a1.a1', '24.be1.a1', '24.bf1.a1', '36.a1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3824, 1085, 7421, 9443, 4155, 572, 8471, 6092], 'generators': [12, 48, 24, 96, 576, 384], 'label': '1152.155815.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '576.8314', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60974343
    {'ambient': '1152.155815', 'aut_centralizer_order': 48, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.e1.a1', 'complements': ['96.bo1.a1', '96.bp1.a1', '96.bo1.a2', '96.bp1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.m1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '48.cb1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4847, 5283, 5778, 5422, 6607, 4245, 5419, 3925], 'generators': [12, 576, 96, 32, 24, 48], 'label': '1152.155815.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.f1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '576.8314', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60974344
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.d1.a1', '24.g1.a1', '24.h1.a1', '24.k1.a1', '24.l1.a1', '24.t1.a1', '24.v1.a1', '36.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6411, -1, 4038, -1, 6929, -1, 3871, -1], 'generators': [1, 384, 96, 2, 648, 48], 'label': '1152.155815.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.g1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974345
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.e1.a1', '576.d1.a1', '576.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.j1.a1', '4.k1.a1', '6.s1.a1', '6.t1.a1', '8.m1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7135, 8931, 3480, 2538, 7687, 5555, 3244, 1400], 'generators': [85, 32, 384, 6, 48, 576, 672, 72], 'label': '1152.155815.2.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.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '576.8314', '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': '576.8314'}
  • id: 60974346
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.h1.a1', '24.j1.a1', '24.l1.a1', '24.x1.a1', '24.bj1.a1', '36.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6189, -1, 4088, -1, 6867, -1, 4009, -1], 'generators': [577, 384, 96, 2, 648, 48], 'label': '1152.155815.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.h1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974347
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.n1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.i1.a1', '24.m1.a1', '24.u1.a1', '24.cf1.a1', '24.cg1.a1', '24.cl1.a1', '36.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3137, -1, 6630, -1, 3024, -1, 6258, -1], 'generators': [1, 384, 48, 2, 72, 96], 'label': '1152.155815.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974348
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.o1.a1'], 'contains': ['24.i1.a1', '24.s1.a1', '24.bh1.a1', '24.ch1.a1', '24.cu1.a1', '36.e1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1209, -1, 9039, -1, 1252, -1, 8334, -1], 'generators': [1, 384, 48, 6, 672, 72], 'label': '1152.155815.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974349
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '24.i1.a1', '24.z1.a1', '24.be1.a1', '24.ci1.a1', '24.db1.a1', '24.dc1.a1', '36.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2850, -1, 7659, -1, 1515, -1, 8973, -1], 'generators': [1, 384, 48, 12, 96, 24], 'label': '1152.155815.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974350
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.n1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.i1.a1', '24.ba1.a1', '24.bd1.a1', '36.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3533, -1, 6062, -1, 4707, -1, 5066, -1], 'generators': [1, 384, 96, 578, 72, 48], 'label': '1152.155815.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974351
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '6.o1.a1'], 'contains': ['24.i1.a1', '24.bb1.a1', '24.bg1.a1', '36.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3292, -1, 6430, -1, 3184, -1, 6551, -1], 'generators': [1, 384, 48, 582, 72, 672], 'label': '1152.155815.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974352
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.i1.a1', '24.bc1.a1', '24.bf1.a1', '24.ci1.a1', '24.dd1.a1', '36.i1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2340, -1, 7758, -1, 2163, -1, 9227, -1], 'generators': [1, 384, 48, 588, 96, 24], 'label': '1152.155815.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974353
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.a1', '6.p1.a1'], 'contains': ['24.m1.a1', '24.s1.a1', '24.be1.a1', '24.cj1.a1', '24.ck1.a1', '36.j1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1913, -1, 8387, -1, 1324, -1, 8542, -1], 'generators': [2, 48, 72, 12, 96, 384], 'label': '1152.155815.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60974354
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.m1.a1', '24.y1.a1', '24.bd1.a1', '36.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2588, -1, 7256, -1, 3726, -1, 5229, -1], 'generators': [577, 384, 96, 2, 72, 48], 'label': '1152.155815.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.p1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974355
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.q1.a1'], 'contains': ['24.m1.a1', '24.z1.a1', '24.bh1.a1', '24.cm1.a1', '24.cn1.a1', '36.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1074, -1, 8525, -1, 1416, -1, 8126, -1], 'generators': [85, 384, 48, 2, 96, 72], 'label': '1152.155815.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.q1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974356
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 4, 'centralizer': '288.a1.a1', 'complements': ['576.e1.a1', '576.f1.a1', '576.d1.a1', '576.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.a1', '4.g1.a1', '6.u1.a1', '6.v1.a1', '6.w1.a1', '8.n1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4848, 4077, 5765, 1235, 6507, 8953, 5482, 5015], 'generators': [3, 32, 384, 12, 48, 576, 96, 24], 'label': '1152.155815.2.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.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '576.8314', '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': '288.1028'}
  • id: 60974357
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.p1.a1'], 'contains': ['24.m1.a1', '24.bb1.a1', '24.bf1.a1', '36.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2769, -1, 7190, -1, 2867, -1, 6667, -1], 'generators': [2, 48, 96, 588, 384, 168], 'label': '1152.155815.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.r1.a1', 'projective_image': '576.8314', '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': '32.46'}
  • id: 60974358
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '6.q1.a1'], 'contains': ['24.m1.a1', '24.bc1.a1', '24.bg1.a1', '24.co1.a1', '36.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2673, -1, 7006, -1, 2350, -1, 7455, -1], 'generators': [661, 384, 48, 2, 96, 168], 'label': '1152.155815.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.s1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974359
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1'], 'contains': ['24.n1.a1', '24.o1.a1', '24.r1.a1', '24.v1.a1', '24.w1.a1', '24.bi1.a1', '24.bl1.a1', '36.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5592, -1, 4482, -1, 5160, -1, 4644, -1], 'generators': [85, 384, 672, 6, 648, 48], 'label': '1152.155815.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.t1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974360
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.q1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bm1.a1', '36.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5528, -1, 4642, -1, 5084, -1, 4778, -1], 'generators': [661, 384, 672, 6, 648, 48], 'label': '1152.155815.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.u1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974361
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.i1.a1', '6.s1.a1'], 'contains': ['24.n1.a1', '24.p1.a1', '24.s1.a1', '24.u1.a1', '24.z1.a1', '24.cr1.a1', '24.cs1.a1', '24.ct1.a1', '36.q1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1972, -1, 8445, -1, 2084, -1, 6741, -1], 'generators': [85, 384, 48, 6, 72, 672], 'label': '1152.155815.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.v1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974362
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.s1.a1', '24.y1.a1', '24.bg1.a1', '24.cv1.a1', '36.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2134, -1, 7835, -1, 1716, -1, 7141, -1], 'generators': [577, 384, 48, 6, 672, 744], 'label': '1152.155815.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.w1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974363
    {'ambient': '1152.155815', 'aut_centralizer_order': 12, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '6.p1.a1'], 'contains': ['24.s1.a1', '24.ba1.a1', '24.bf1.a1', '36.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1854, -1, 8604, -1, 2449, -1, 7716, -1], 'generators': [578, 48, 96, 588, 384, 168], 'label': '1152.155815.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.x1.a1', 'projective_image': '576.8314', '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: 60974364
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.g1.a1', '6.s1.a1'], 'contains': ['24.q1.a1', '24.r1.a1', '24.s1.a1', '24.bc1.a1', '24.bd1.a1', '36.t1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2446, -1, 7588, -1, 3652, -1, 6418, -1], 'generators': [661, 384, 672, 6, 72, 48], 'label': '1152.155815.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974365
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.t1.a1', '24.u1.a1', '24.x1.a1', '24.y1.a1', '24.ba1.a1', '36.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2514, -1, 6922, -1, 3796, -1, 5295, -1], 'generators': [577, 384, 96, 578, 72, 48], 'label': '1152.155815.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974366
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1', '6.s1.a1'], 'contains': ['24.u1.a1', '24.w1.a1', '24.bb1.a1', '24.bc1.a1', '24.bm1.a1', '36.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3056, -1, 6777, -1, 3914, -1, 6184, -1], 'generators': [661, 384, 672, 582, 72, 48], 'label': '1152.155815.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974367
    {'ambient': '1152.155815', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1090146', 'aut_weyl_index': 6, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.r1.a1', '6.t1.a1', '6.v1.a1', '9.a1.a1', '12.cf1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6546, -1, 4835, -1, 7339, -1, 3652, -1], 'generators': [1, 48, 32, 2, 24, 576, 96, 12], 'label': '1152.155815.3.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': '576.8314', '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': '192.1472'}
  • id: 60974368
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.j1.a1', '6.u1.a1'], 'contains': ['24.u1.a1', '24.be1.a1', '24.bh1.a1', '24.cx1.a1', '24.cy1.a1', '36.w1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1279, -1, 9107, -1, 1801, -1, 8615, -1], 'generators': [3, 384, 48, 12, 96, 24], 'label': '1152.155815.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bb1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974369
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '6.u1.a1'], 'contains': ['24.u1.a1', '24.bf1.a1', '24.bg1.a1', '36.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1707, -1, 8653, -1, 2693, -1, 7773, -1], 'generators': [3, 384, 48, 588, 24, 96], 'label': '1152.155815.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bc1.a1', 'projective_image': '576.8314', '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': '48.51'}
  • id: 60974370
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.y1.a1', '24.z1.a1', '24.bf1.a1', '24.db1.a1', '24.dd1.a1', '36.y1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1758, -1, 8329, -1, 1593, -1, 8900, -1], 'generators': [577, 384, 48, 588, 96, 24], 'label': '1152.155815.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bd1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974371
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.y1.a1', '24.bb1.a1', '24.bh1.a1', '36.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1616, -1, 7315, -1, 2639, -1, 6886, -1], 'generators': [577, 384, 48, 582, 744, 672], 'label': '1152.155815.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.be1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974372
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '6.j1.a1'], 'contains': ['24.y1.a1', '24.bc1.a1', '24.be1.a1', '24.dc1.a1', '24.dd1.a1', '36.ba1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2053, -1, 7487, -1, 2005, -1, 9153, -1], 'generators': [577, 384, 48, 12, 96, 24], 'label': '1152.155815.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bf1.a1', 'projective_image': '576.8314', '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': '48.38'}
  • id: 60974373
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.q1.a1'], 'contains': ['24.z1.a1', '24.ba1.a1', '24.bg1.a1', '36.bb1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3242, -1, 6496, -1, 2743, -1, 7021, -1], 'generators': [85, 384, 48, 578, 72, 96], 'label': '1152.155815.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bg1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974374
    {'ambient': '1152.155815', 'aut_centralizer_order': 8, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.s1.a1'], 'contains': ['24.z1.a1', '24.bb1.a1', '24.bd1.a1', '24.bk1.a1', '24.bl1.a1', '36.bc1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3622, -1, 6149, -1, 3985, -1, 5150, -1], 'generators': [85, 384, 672, 582, 72, 48], 'label': '1152.155815.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bh1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974375
    {'ambient': '1152.155815', 'aut_centralizer_order': 24, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.p1.a1'], 'contains': ['24.ba1.a1', '24.bb1.a1', '24.be1.a1', '36.bd1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3351, -1, 6355, -1, 3113, -1, 6484, -1], 'generators': [578, 48, 96, 12, 384, 72], 'label': '1152.155815.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bi1.a1', 'projective_image': '576.8314', '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: 60974376
    {'ambient': '1152.155815', 'aut_centralizer_order': 4, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '6.q1.a1'], 'contains': ['24.ba1.a1', '24.bc1.a1', '24.bh1.a1', '36.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1665, -1, 7363, -1, 2517, -1, 7653, -1], 'generators': [661, 384, 48, 578, 168, 96], 'label': '1152.155815.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bj1.a1', 'projective_image': '576.8314', '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': '96.209'}
  • id: 60974377
    {'ambient': '1152.155815', 'aut_centralizer_order': 16, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.u1.a1'], 'contains': ['24.bd1.a1', '24.be1.a1', '24.bg1.a1', '36.bf1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2395, -1, 7904, -1, 2799, -1, 8003, -1], 'generators': [579, 384, 48, 12, 24, 96], 'label': '1152.155815.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bk1.a1', 'projective_image': '576.8314', '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': '48.51'}