Abstract group data - 1152.156064

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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, 16, 96, 192], [129, 138, 208, 576, 288], [1, 2, 24, 96, 960], [33, 34, 16, 576, 288], [73, 66, 1136, 96, 1056], [673, 674, 112, 96, 192], [685, 678, 1048, 576, 864], [673, 674, 688, 96, 192], [1, 2, 784, 96, 192], [649, 646, 944, 96, 288], [1, 2, 88, 576, 864], [1, 2, 88, 576, 480]], 'aut_group': '4608.lj', 'aut_hash': 3301011005301566777, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 34, 'aut_perms': [157481167662188173055559121084818700552, 104585591738656721513520, 78526551667740106459962026505998343458, 200971231408581164788238105270381181938, 269702240270113326333690447181959127981, 26337761332304957454716875697054237143, 269702240276175107885355324619629402349, 388959370560288574426800, 177256892300897492015552796932997311090, 3653979489591668474967397466, 3653979489591794534776308506], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 4, 1, 1], [2, 9, 2, 1], [2, 12, 1, 2], [2, 36, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 18, 1, 1], [4, 24, 1, 2], [4, 72, 1, 2], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 2], [6, 16, 1, 1], [6, 16, 2, 1], [6, 24, 1, 1], [6, 24, 2, 1], [6, 32, 2, 1], [6, 48, 2, 1], [8, 12, 2, 2], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 32, 1, 1], [12, 48, 1, 3], [24, 24, 2, 2]], '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, 4], [2, 4, 1], [2, 9, 2], [2, 12, 2], [2, 36, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 2, 1], [4, 6, 2], [4, 18, 1], [4, 24, 2], [4, 72, 2], [6, 2, 1], [6, 6, 2], [6, 8, 2], [6, 16, 3], [6, 24, 3], [6, 32, 2], [6, 48, 2], [8, 12, 4], [8, 36, 4], [12, 4, 1], [12, 12, 1], [12, 16, 1], [12, 32, 1], [12, 48, 3], [24, 24, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '576.8353', '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': 156064, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['192.973', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 4, 1, 1], [2, 9, 1, 2], [2, 12, 1, 2], [2, 36, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 18, 1, 1], [4, 24, 1, 2], [4, 72, 1, 2], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 2], [6, 16, 1, 1], [6, 16, 2, 1], [6, 24, 1, 3], [6, 32, 2, 1], [6, 48, 2, 1], [8, 12, 2, 2], [8, 36, 2, 2], [12, 4, 1, 1], [12, 12, 1, 1], [12, 16, 1, 1], [12, 32, 1, 1], [12, 48, 1, 3], [24, 24, 2, 2]], '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': 156064, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 6, 2, 6], 'inner_gens': [[1, 6, 80, 576, 864], [13, 2, 80, 576, 864], [33, 34, 16, 576, 1056], [673, 674, 688, 96, 192], [673, 674, 496, 96, 192]], 'inner_hash': 8353, 'inner_nilpotent': False, 'inner_order': 576, 'inner_split': True, 'inner_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/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, 18], [3, 8], [4, 9], [6, 10], [8, 1], [12, 3]], 'label': '1152.156064', 'linC_count': 144, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 128, 'linQ_dim': 9, 'linQ_dim_count': 64, 'linR_count': 64, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D6.GL(2,Z/4)', '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': 45, 'number_characteristic_subgroups': 53, 'number_conjugacy_classes': 57, 'number_divisions': 48, 'number_normal_subgroups': 59, 'number_subgroup_autclasses': 648, 'number_subgroup_classes': 734, 'number_subgroups': 6886, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 95], [3, 26], [4, 224], [6, 310], [8, 192], [12, 208], [24, 96]], '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': [[1, 2, 88, 576, 480], [1, 10, 16, 96, 192], [1, 2, 80, 576, 864]], '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, 9], [6, 6], [8, 3], [12, 3], [24, 1]], 'representations': {'PC': {'code': '1325371648818570224623111721489501314952873441261892651933918071157488561673', 'gens': [1, 2, 5, 7, 8], 'pres': [9, -2, -2, -2, -2, -2, -3, -2, 2, -3, 72, 109, 46, 326, 74, 3604, 1813, 130, 3461, 1742, 36294, 18159, 2310, 1374, 62215, 31120, 4795, 1996, 214, 3932]}, 'Perm': {'d': 15, 'gens': [120, 100721335685, 21156670080, 200386730880, 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': 'D_6.\\GL(2,\\mathbb{Z}/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: 108501794
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 156064, 'group_order': 1152, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 108501805
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 156064, 'group_order': 1152, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 8, 'size': 1}
  • id: 108501816
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 3, 'group_counter': 156064, 'group_order': 1152, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 576, 'size': 3}
  • id: 108501827
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 156064, 'group_order': 1152, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 48, 'size': 3}
  • id: 108501838
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 5, 'group_counter': 156064, 'group_order': 1152, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 56, 'size': 3}
  • id: 108501847
    {'aut_label': '2E', 'centralizer': '3.b1.a1', 'counter': 6, 'group_counter': 156064, 'group_order': 1152, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 680, 'size': 3}
  • id: 108501848
    {'aut_label': '2F', 'centralizer': '4.h1.a1', 'counter': 7, 'group_counter': 156064, 'group_order': 1152, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 3, 'size': 4}
  • id: 108501849
    {'aut_label': '2G', 'centralizer': '9.a1.a1', 'counter': 8, 'group_counter': 156064, 'group_order': 1152, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 240, 'size': 9}
  • id: 108501850
    {'aut_label': '2G', 'centralizer': '9.a1.a1', 'counter': 9, 'group_counter': 156064, 'group_order': 1152, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 248, 'size': 9}
  • id: 108501795
    {'aut_label': '2I', 'centralizer': '12.bp1.a1', 'counter': 10, 'group_counter': 156064, 'group_order': 1152, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 579, 'size': 12}
  • id: 108501796
    {'aut_label': '2J', 'centralizer': '12.bm1.a1', 'counter': 11, 'group_counter': 156064, 'group_order': 1152, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 823, 'size': 12}
  • id: 108501797
    {'aut_label': '2K', 'centralizer': '36.bh1.a1', 'counter': 12, 'group_counter': 156064, 'group_order': 1152, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 635, 'size': 36}
  • id: 108501798
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 13, 'group_counter': 156064, 'group_order': 1152, 'label': '3A', 'order': 3, 'powers': [13, 1], 'representative': 384, 'size': 2}
  • id: 108501799
    {'aut_label': '3B', 'centralizer': '8.h1.a1', 'counter': 14, 'group_counter': 156064, 'group_order': 1152, 'label': '3B', 'order': 3, 'powers': [14, 1], 'representative': 64, 'size': 8}
  • id: 108501800
    {'aut_label': '3C', 'centralizer': '16.g1.a1', 'counter': 15, 'group_counter': 156064, 'group_order': 1152, 'label': '3C', 'order': 3, 'powers': [15, 1], 'representative': 832, 'size': 16}
  • id: 108501801
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 156064, 'group_order': 1152, 'label': '4A', 'order': 4, 'powers': [2, 16], 'representative': 12, 'size': 2}
  • id: 108501802
    {'aut_label': '4B', 'centralizer': '6.o1.a1', 'counter': 17, 'group_counter': 156064, 'group_order': 1152, 'label': '4B', 'order': 4, 'powers': [2, 17], 'representative': 684, 'size': 6}
  • id: 108501803
    {'aut_label': '4C', 'centralizer': '6.m1.a1', 'counter': 18, 'group_counter': 156064, 'group_order': 1152, 'label': '4C', 'order': 4, 'powers': [2, 18], 'representative': 828, 'size': 6}
  • id: 108501804
    {'aut_label': '4D', 'centralizer': '18.k1.a1', 'counter': 19, 'group_counter': 156064, 'group_order': 1152, 'label': '4D', 'order': 4, 'powers': [2, 19], 'representative': 244, 'size': 18}
  • id: 108501806
    {'aut_label': '4E', 'centralizer': '24.j1.a1', 'counter': 20, 'group_counter': 156064, 'group_order': 1152, 'label': '4E', 'order': 4, 'powers': [6, 20], 'representative': 161, 'size': 24}
  • id: 108501807
    {'aut_label': '4F', 'centralizer': '24.k1.a1', 'counter': 21, 'group_counter': 156064, 'group_order': 1152, 'label': '4F', 'order': 4, 'powers': [2, 21], 'representative': 37, 'size': 24}
  • id: 108501808
    {'aut_label': '4G', 'centralizer': '72.f1.a1', 'counter': 22, 'group_counter': 156064, 'group_order': 1152, 'label': '4G', 'order': 4, 'powers': [6, 22], 'representative': 1017, 'size': 72}
  • id: 108501809
    {'aut_label': '4H', 'centralizer': '72.g1.a1', 'counter': 23, 'group_counter': 156064, 'group_order': 1152, 'label': '4H', 'order': 4, 'powers': [2, 23], 'representative': 573, 'size': 72}
  • id: 108501810
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 24, 'group_counter': 156064, 'group_order': 1152, 'label': '6A', 'order': 6, 'powers': [13, 2], 'representative': 392, 'size': 2}
  • id: 108501811
    {'aut_label': '6B', 'centralizer': '6.p1.a1', 'counter': 25, 'group_counter': 156064, 'group_order': 1152, 'label': '6B', 'order': 6, 'powers': [13, 3], 'representative': 192, 'size': 6}
  • id: 108501812
    {'aut_label': '6C', 'centralizer': '6.p1.a1', 'counter': 26, 'group_counter': 156064, 'group_order': 1152, 'label': '6C', 'order': 6, 'powers': [13, 6], 'representative': 968, 'size': 6}
  • id: 108501813
    {'aut_label': '6D', 'centralizer': '8.d1.a1', 'counter': 27, 'group_counter': 156064, 'group_order': 1152, 'label': '6D', 'order': 6, 'powers': [13, 7], 'representative': 387, 'size': 8}
  • id: 108501814
    {'aut_label': '6E', 'centralizer': '8.h1.a1', 'counter': 28, 'group_counter': 156064, 'group_order': 1152, 'label': '6E', 'order': 6, 'powers': [14, 2], 'representative': 72, 'size': 8}
  • id: 108501815
    {'aut_label': '6F', 'centralizer': '16.g1.a1', 'counter': 29, 'group_counter': 156064, 'group_order': 1152, 'label': '6F', 'order': 6, 'powers': [15, 2], 'representative': 840, 'size': 16}
  • id: 108501817
    {'aut_label': '6G1', 'centralizer': '16.c1.a1', 'counter': 30, 'group_counter': 156064, 'group_order': 1152, 'label': '6G1', 'order': 6, 'powers': [14, 7], 'representative': 35, 'size': 16}
  • id: 108501818
    {'aut_label': '6G1', 'centralizer': '16.c1.a1', 'counter': 31, 'group_counter': 156064, 'group_order': 1152, 'label': '6G-1', 'order': 6, 'powers': [14, 7], 'representative': 67, 'size': 16}
  • id: 108501819
    {'aut_label': '6H', 'centralizer': '24.cc1.a1', 'counter': 32, 'group_counter': 156064, 'group_order': 1152, 'label': '6H', 'order': 6, 'powers': [14, 4], 'representative': 16, 'size': 24}
  • id: 108501820
    {'aut_label': '6H', 'centralizer': '24.cc1.a1', 'counter': 33, 'group_counter': 156064, 'group_order': 1152, 'label': '6I', 'order': 6, 'powers': [14, 5], 'representative': 24, 'size': 24}
  • id: 108501821
    {'aut_label': '6J', 'centralizer': '24.bq1.a1', 'counter': 34, 'group_counter': 156064, 'group_order': 1152, 'label': '6J', 'order': 6, 'powers': [13, 10], 'representative': 195, 'size': 24}
  • id: 108501822
    {'aut_label': '6K1', 'centralizer': '32.c1.a1', 'counter': 35, 'group_counter': 156064, 'group_order': 1152, 'label': '6K1', 'order': 6, 'powers': [15, 7], 'representative': 419, 'size': 32}
  • id: 108501823
    {'aut_label': '6K1', 'centralizer': '32.c1.a1', 'counter': 36, 'group_counter': 156064, 'group_order': 1152, 'label': '6K-1', 'order': 6, 'powers': [15, 7], 'representative': 451, 'size': 32}
  • id: 108501824
    {'aut_label': '6L1', 'centralizer': '48.v1.a1', 'counter': 37, 'group_counter': 156064, 'group_order': 1152, 'label': '6L1', 'order': 6, 'powers': [14, 11], 'representative': 887, 'size': 48}
  • id: 108501825
    {'aut_label': '6L1', 'centralizer': '48.v1.a1', 'counter': 38, 'group_counter': 156064, 'group_order': 1152, 'label': '6L-1', 'order': 6, 'powers': [14, 11], 'representative': 375, 'size': 48}
  • id: 108501826
    {'aut_label': '8A1', 'centralizer': '12.l1.a1', 'counter': 39, 'group_counter': 156064, 'group_order': 1152, 'label': '8A1', 'order': 8, 'powers': [16, 39], 'representative': 6, 'size': 12}
  • id: 108501828
    {'aut_label': '8A1', 'centralizer': '12.l1.a1', 'counter': 40, 'group_counter': 156064, 'group_order': 1152, 'label': '8A-1', 'order': 8, 'powers': [16, 40], 'representative': 10, 'size': 12}
  • id: 108501829
    {'aut_label': '8B1', 'centralizer': '12.m1.a1', 'counter': 41, 'group_counter': 156064, 'group_order': 1152, 'label': '8B1', 'order': 8, 'powers': [17, 41], 'representative': 102, 'size': 12}
  • id: 108501830
    {'aut_label': '8B1', 'centralizer': '12.m1.a1', 'counter': 42, 'group_counter': 156064, 'group_order': 1152, 'label': '8B-1', 'order': 8, 'powers': [17, 42], 'representative': 586, 'size': 12}
  • id: 108501831
    {'aut_label': '8C1', 'centralizer': '36.h1.a1', 'counter': 43, 'group_counter': 156064, 'group_order': 1152, 'label': '8C1', 'order': 8, 'powers': [17, 43], 'representative': 1078, 'size': 36}
  • id: 108501832
    {'aut_label': '8C1', 'centralizer': '36.h1.a1', 'counter': 44, 'group_counter': 156064, 'group_order': 1152, 'label': '8C-1', 'order': 8, 'powers': [17, 44], 'representative': 506, 'size': 36}
  • id: 108501833
    {'aut_label': '8D1', 'centralizer': '36.g1.a1', 'counter': 45, 'group_counter': 156064, 'group_order': 1152, 'label': '8D1', 'order': 8, 'powers': [16, 45], 'representative': 830, 'size': 36}
  • id: 108501834
    {'aut_label': '8D1', 'centralizer': '36.g1.a1', 'counter': 46, 'group_counter': 156064, 'group_order': 1152, 'label': '8D-1', 'order': 8, 'powers': [16, 46], 'representative': 818, 'size': 36}
  • id: 108501835
    {'aut_label': '12A', 'centralizer': '4.f1.a1', 'counter': 47, 'group_counter': 156064, 'group_order': 1152, 'label': '12A', 'order': 12, 'powers': [24, 16], 'representative': 772, 'size': 4}
  • id: 108501836
    {'aut_label': '12B', 'centralizer': '12.bx1.a1', 'counter': 48, 'group_counter': 156064, 'group_order': 1152, 'label': '12B', 'order': 12, 'powers': [24, 17], 'representative': 1060, 'size': 12}
  • id: 108501837
    {'aut_label': '12C', 'centralizer': '16.d1.a1', 'counter': 49, 'group_counter': 156064, 'group_order': 1152, 'label': '12C', 'order': 12, 'powers': [28, 16], 'representative': 36, 'size': 16}
  • id: 108501839
    {'aut_label': '12D', 'centralizer': '32.e1.a1', 'counter': 50, 'group_counter': 156064, 'group_order': 1152, 'label': '12D', 'order': 12, 'powers': [29, 16], 'representative': 420, 'size': 32}
  • id: 108501840
    {'aut_label': '12E', 'centralizer': '48.w1.a1', 'counter': 51, 'group_counter': 156064, 'group_order': 1152, 'label': '12E', 'order': 12, 'powers': [28, 18], 'representative': 308, 'size': 48}
  • id: 108501841
    {'aut_label': '12F', 'centralizer': '48.q1.a1', 'counter': 52, 'group_counter': 156064, 'group_order': 1152, 'label': '12F', 'order': 12, 'powers': [26, 20], 'representative': 361, 'size': 48}
  • id: 108501842
    {'aut_label': '12G', 'centralizer': '48.r1.a1', 'counter': 53, 'group_counter': 156064, 'group_order': 1152, 'label': '12G', 'order': 12, 'powers': [24, 21], 'representative': 813, 'size': 48}
  • id: 108501843
    {'aut_label': '24A1', 'centralizer': '24.bf1.a1', 'counter': 54, 'group_counter': 156064, 'group_order': 1152, 'label': '24A1', 'order': 24, 'powers': [47, 39], 'representative': 386, 'size': 24}
  • id: 108501844
    {'aut_label': '24A1', 'centralizer': '24.bf1.a1', 'counter': 55, 'group_counter': 156064, 'group_order': 1152, 'label': '24A-1', 'order': 24, 'powers': [47, 40], 'representative': 394, 'size': 24}
  • id: 108501845
    {'aut_label': '24B1', 'centralizer': '24.bg1.a1', 'counter': 56, 'group_counter': 156064, 'group_order': 1152, 'label': '24B1', 'order': 24, 'powers': [48, 41], 'representative': 194, 'size': 24}
  • id: 108501846
    {'aut_label': '24B1', 'centralizer': '24.bg1.a1', 'counter': 57, 'group_counter': 156064, 'group_order': 1152, 'label': '24B-1', 'order': 24, 'powers': [48, 42], 'representative': 202, 'size': 24}
• 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: 3898180
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1a', '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, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898191
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1b', '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, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898202
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1c', '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, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898213
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1d', '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, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898223
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1e', '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, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898224
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1f', '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, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898225
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1g', '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, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898226
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.1h', '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, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898227
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, 2, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 2, -1, 2, 2, 0, -1, 0, -1, -1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, -1, 0, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898181
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898182
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, 0, -2, -2, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898183
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898184
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, -1, -1, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, -2, -1, -1, 1, 1, 1, -2, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898185
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -1, -1, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 1, 2, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898186
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, -2, 0, 0, -2, 0, 0, -1, 2, -1, 2, 2, 0, 0, -2, -2, 0, 0, -1, -1, -1, 1, 2, -1, -2, -2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, 1, 0, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3898187
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, -2, 0, 0, -2, 0, 0, -1, 2, -1, 2, 2, 0, 0, 2, 2, 0, 0, -1, -1, -1, 1, 2, -1, -2, -2, 0, 1, 0, 1, 1, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, 2, -1, -1, 0, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898188
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, 2, 0, 0, -2, -2, 0, 0, -1, -1, -1, -1, 2, -1, 2, 2, 0, -1, 0, -1, -1, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, 2, -1, 1, 0, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3898189
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, -2, -1, -1, 1, 1, -1, -2, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898195
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, 3, -1, -1, -1, 3, -1, 3, 0, 0, 3, -1, 3, -1, -1, 1, -1, 1, 3, -1, -1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, -1, -1, 3, -1, 0, 0, 1, 0, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898196
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, 3, -1, -1, -1, 3, -1, 3, 0, 0, 3, -1, 3, -1, 1, -1, 1, -1, 3, -1, -1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, 1, 3, -1, 0, 0, -1, 0, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898197
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, -3, -3, 1, 1, 1, 3, -1, 3, 0, 0, 3, -1, -3, 1, -1, 1, 1, -1, 3, -1, -1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, -1, 3, -1, 0, 0, 1, 0, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898198
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, -3, -3, 1, 1, 1, 3, -1, 3, 0, 0, 3, -1, -3, 1, 1, -1, -1, 1, 3, -1, -1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, 1, 3, -1, 0, 0, -1, 0, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898199
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, -3, 3, 1, 1, -1, -3, 1, 3, 0, 0, 3, -1, -3, 1, -1, 1, 1, -1, 3, -1, -1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, 1, 3, -1, 0, 0, 1, 0, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898200
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, -3, 3, 1, 1, -1, -3, 1, 3, 0, 0, 3, -1, -3, 1, 1, -1, -1, 1, 3, -1, -1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, -1, 3, -1, 0, 0, -1, 0, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898201
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, -3, -1, -1, 1, -3, 1, 3, 0, 0, 3, -1, 3, -1, -1, 1, -1, 1, 3, -1, -1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, 1, 3, -1, 0, 0, 1, 0, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898203
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, -3, -1, -1, 1, -3, 1, 3, 0, 0, 3, -1, 3, -1, 1, -1, 1, -1, 3, -1, -1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, -1, -1, 3, -1, 0, 0, -1, 0, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898190
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2k', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 0, 4, -4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, -4, -4, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898192
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2l', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, -4, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, -4, -4, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898193
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2m', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 4, -4, 0, -4, -4, 0, 0, 0, 4, -2, -2, -4, -4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 0, -2, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898194
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.2n', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, 4, -2, -2, -4, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 0, -2, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898204
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 0, 4, 0, 0, 4, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, -2, -2, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898205
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898206
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4c', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 0, -4, 0, 0, -4, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, 1, 2, 2, 0, 2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898207
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4d', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 0, 4, -4, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 3898208
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4e', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, -4, 4, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, 2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 3898211
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6a', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, 6, -6, -2, -2, -6, 0, 2, 2, 0, 0, 0, 6, 0, 0, -6, 2, 6, -2, 0, 0, 0, 0, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898212
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6b', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, 6, 6, -2, -2, 6, 0, -2, -2, 0, 0, 0, 6, 0, 0, -6, 2, -6, 2, 0, 0, 0, 0, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898214
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6c', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 0, 6, 0, 0, -2, 0, 0, -3, 0, 0, 6, -2, 0, 0, -2, 2, 0, 0, -3, 1, 1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, -3, 1, 0, 0, -1, 0, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898215
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6d', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 0, 6, 0, 0, -2, 0, 0, -3, 0, 0, 6, -2, 0, 0, 2, -2, 0, 0, -3, 1, 1, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, -3, 1, 0, 0, 1, 0, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898216
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6e', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 0, -6, 0, 0, 2, 0, 0, -3, 0, 0, 6, -2, 0, 0, -2, 2, 0, 0, -3, 1, 1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, -3, 1, 0, 0, -1, 0, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3898217
    {'cdim': 6, 'counter': 43, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6f', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 0, -6, 0, 0, 2, 0, 0, -3, 0, 0, 6, -2, 0, 0, 2, -2, 0, 0, -3, 1, 1, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, -3, 1, 0, 0, 1, 0, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3898209
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4f', 'multiplicity': 2, 'nt': [24, 142], 'qdim': 8, 'qvalues': [8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, -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, 0, 0, 0], 'schur_index': 1}
  • id: 3898210
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.4g', 'multiplicity': 2, 'nt': [24, 204], 'qdim': 8, 'qvalues': [8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898220
    {'cdim': 8, 'counter': 46, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.8a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 4, -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], 'schur_index': 2}
  • id: 3898218
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6g', 'multiplicity': 2, 'nt': [24, 331], 'qdim': 12, 'qvalues': [12, -12, -12, 4, -4, 12, 0, -4, 4, 0, 0, 0, 12, 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, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898219
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.6h', 'multiplicity': 2, 'nt': [24, 331], 'qdim': 12, 'qvalues': [12, -12, 12, 4, -4, -12, 0, 4, -4, 0, 0, 0, 12, 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, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898221
    {'cdim': 12, 'counter': 47, 'faithful': False, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.12a', 'multiplicity': 1, 'nt': [36, 768], 'qdim': 12, 'qvalues': [12, 12, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -12, 4, 0, 0, 0, 0, 0, 0, -6, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3898222
    {'cdim': 12, 'counter': 48, 'faithful': True, 'group': '1152.156064', 'group_order': 1152, 'image': None, 'label': '1152.156064.12b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, -12, 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, 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: 5409491
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1152, 'label': '1152.156064.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409502
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 576, 'label': '1152.156064.1b', '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]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409513
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 576, 'label': '1152.156064.1c', '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]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409524
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 576, 'label': '1152.156064.1d', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409535
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 576, 'label': '1152.156064.1e', '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]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409544
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 576, 'label': '1152.156064.1f', '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]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409545
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 576, 'label': '1152.156064.1g', '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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409546
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 576, 'label': '1152.156064.1h', '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]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409547
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 192, 'label': '1152.156064.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409492
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 192, 'label': '1152.156064.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409493
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 288, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 144, 'label': '1152.156064.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409494
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 288, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 144, 'label': '1152.156064.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409495
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 96, 'label': '1152.156064.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409496
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 96, 'label': '1152.156064.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409497
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 96, 'label': '1152.156064.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409498
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 96, 'label': '1152.156064.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409499
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 96, 'label': '1152.156064.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409500
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 96, 'label': '1152.156064.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409501
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 19, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 72, 'label': '1152.156064.2k1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409503
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 20, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 72, 'label': '1152.156064.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5409504
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 72, 'label': '1152.156064.2l1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409505
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 72, 'label': '1152.156064.2l2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5409506
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 48, 'label': '1152.156064.2m1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409507
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 48, 'label': '1152.156064.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409508
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 48, 'label': '1152.156064.2n1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409509
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 48, 'label': '1152.156064.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409510
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 48, 'label': '1152.156064.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409511
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 48, 'label': '1152.156064.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409512
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.156064.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409514
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.156064.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409515
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.156064.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409516
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.156064.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409517
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 24, 'label': '1152.156064.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409518
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 24, 'label': '1152.156064.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 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]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409519
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 32, 'label': '1152.156064.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409520
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 48, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 24, 'label': '1152.156064.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409521
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 16, 'label': '1152.156064.4c', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409522
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.f1.a1', 'kernel_order': 24, 'label': '1152.156064.4d', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409523
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.f1.b1', 'kernel_order': 24, 'label': '1152.156064.4e', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409525
    {'center': '48.b1.a1', 'center_index': 48, 'center_order': 24, 'counter': 40, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '96.120', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.a1', 'kernel_order': 12, 'label': '1152.156064.4f1', 'nt': [24, 142], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5409526
    {'center': '48.b1.a1', 'center_index': 48, 'center_order': 24, 'counter': 41, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '96.120', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.a1', 'kernel_order': 12, 'label': '1152.156064.4f2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409527
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.156064.4g1', 'nt': [24, 204], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409528
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.156064.4g2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5409529
    {'center': '48.c1.a1', 'center_index': 48, 'center_order': 24, 'counter': 44, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1.a1', 'kernel_order': 12, 'label': '1152.156064.6a', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[6, 0]], [[-2, 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]], [[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]]]}
  • id: 5409530
    {'center': '48.c1.a1', 'center_index': 48, 'center_order': 24, 'counter': 45, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 12, 'label': '1152.156064.6b', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[2, 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]], [[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]]]}
  • id: 5409531
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 46, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.156064.6c', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409532
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.156064.6d', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409533
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.156064.6e', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5409534
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.156064.6f', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5409536
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 50, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '192.973', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 6, 'label': '1152.156064.6g1', 'nt': [24, 331], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[-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]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5409537
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 51, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '192.973', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 6, 'label': '1152.156064.6g2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[-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]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409538
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 52, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '192.973', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.b1', 'kernel_order': 6, 'label': '1152.156064.6h1', 'nt': [24, 331], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[-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]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5409539
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 53, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '192.973', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.b1', 'kernel_order': 6, 'label': '1152.156064.6h2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[-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]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409540
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '288.576', 'image_order': 288, 'indicator': -1, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.156064.8a', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 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]], [[0, 0]], [[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: 5409541
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '576.8353', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 2, 'label': '1152.156064.12a', 'nt': [36, 768], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[-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]], [[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]]]}
  • id: 5409542
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 56, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.156064', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.156064.12b1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5409543
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 57, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '1152.156064', 'group_counter': 156064, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.156064', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.156064.12b2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
• 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: 60982944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1152, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1152.156064.1.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': '1152.156064', 'subgroup_hash': 6446418664246003612, 'subgroup_order': 1152, 'subgroup_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60983055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '576.8493', 'subgroup_hash': 8493, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.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': '576.8305', 'subgroup_hash': 8305, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60983277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 576, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5063', 'subgroup_hash': 5063, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60983388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5482', 'subgroup_hash': 5482, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60983499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.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': '576.5530', 'subgroup_hash': 5530, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60983610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.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': '576.5067', 'subgroup_hash': 5067, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60983656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.2.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': '576.5068', 'subgroup_hash': 5068, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60983667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.3.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': '384.18063', 'subgroup_hash': 18063, 'subgroup_order': 384, 'subgroup_tex': 'C_4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 60982945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.3.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': '384.12720', 'subgroup_hash': 12720, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.919', 'subgroup_hash': 919, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '288.980', 'subgroup_hash': 980, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 60982978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': 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: 60982989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.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': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.896', 'subgroup_hash': 896, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.907', 'subgroup_hash': 907, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 288, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.398', 'subgroup_hash': 398, 'subgroup_order': 288, 'subgroup_tex': 'A_4:C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 60983022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.4.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: 60983033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.4.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': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '288.928', 'subgroup_hash': 928, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.4.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': '288.852', 'subgroup_hash': 852, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 60983078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.4.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': '288.576', 'subgroup_hash': 576, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.6.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 192, 'counter': 24, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.156064.6.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': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60983111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.1468', 'subgroup_hash': 1468, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '192.967', 'subgroup_hash': 967, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60983233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.1185', 'subgroup_hash': 1185, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.283', 'subgroup_hash': 283, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.883', 'subgroup_hash': 883, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.777', 'subgroup_hash': 777, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60983289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60983300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.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': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60983311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 60983322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '192.605', 'subgroup_hash': 605, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '192.290', 'subgroup_hash': 290, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 144, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.8.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: 60983366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 60983389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60983411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.137', 'subgroup_hash': 137, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.52', 'subgroup_hash': 52, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.81', 'subgroup_hash': 81, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.97', 'subgroup_hash': 97, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.58', 'subgroup_hash': 58, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.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': '144.59', 'subgroup_hash': 59, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60983511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1152.156064.9.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': '128.1729', 'subgroup_hash': 1729, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 60983533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 96, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.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': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': False, '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: 60983566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.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': 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: 60983577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60983588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60983599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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: 60983633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.104', 'subgroup_hash': 104, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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: 60983672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60982946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60982949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60982952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60982958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60982959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.48', 'subgroup_hash': 48, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60982960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.37', 'subgroup_hash': 37, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60982961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60982963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60982964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60982965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60982966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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: 60982968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.ci1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.12.cl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 72, 'counter': 129, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.16.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: 60982979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 130, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60982980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 131, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60982981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60982983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60982984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60982985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60982986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.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: 60982987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60982988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60982990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60982991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.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: 60982992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60982993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60982995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60982996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60982998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60982999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.87', 'subgroup_hash': 87, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.18.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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 48, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60983013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 161, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60983015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.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: 60983016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 164, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.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': False, '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: 60983017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60983048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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: 60983077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ch1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.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: 60983080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': 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: 60983087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cu1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.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: 60983096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cx1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1.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: 60983101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.de1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.df1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1.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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60983123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.do1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 60983128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.24.dq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 36, 'counter': 266, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.32.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': '32.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\SD_{16}', '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: 60983130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.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: 60983131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.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: 60983134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.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: 60983137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.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: 60983138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 32, 'counter': 276, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.36.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': False, '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: 60983141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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: 60983145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983147
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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: 60983169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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: 60983170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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: 60983171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983177
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 60983179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 16, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bt1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bt1.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': 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: 60983193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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: 60983195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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: 60983196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.36.bw1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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: 60983197
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 327, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.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': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6: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: 60983198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.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: 60983199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, '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: 60983202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 332, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60983204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 333, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60983205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bk1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.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: 60983240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.br1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.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: 60983249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bt1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1.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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bx1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983260
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 384, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60983261
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983264
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 388, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60983265
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983271
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983272
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983275
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.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: 60983281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983284
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983293
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.de1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.de1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.df1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.48.dg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 60983309
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.64.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: 60983310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.64.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: 60983312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.64.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: 60983315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 16, 'counter': 433, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.72.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: 60983316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983318
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60983359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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: 60983364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bu1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bu1.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: 60983368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ca1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ca1.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: 60983375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ce1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ce1.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: 60983381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ch1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ch1.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: 60983385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.co1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cp1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cp1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cu1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cu1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cv1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60983406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 60983409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.72.cx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': True, 'core_order': 12, 'counter': 519, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.195', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 195, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,\\mathbb{Z}/4)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983412
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 12, 'counter': 520, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.156064.96.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': '96.226', '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: 60983413
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 521, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.195', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 195, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,\\mathbb{Z}/4)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60983414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 522, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.140', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 140, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:\\SD_{16}', '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: 60983415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 523, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.120', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 120, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times \\SD_{16}', '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: 60983416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983427
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 534, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983428
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983429
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 536, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983430
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983431
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 538, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983432
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 539, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983434
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983435
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983436
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 542, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60983437
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60983449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60983456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.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: 60983463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 567, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60983464
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60983465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60983467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60983469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60983470
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60983471
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bu1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bu1.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: 60983472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.96.bu1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bu1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60983474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1152.156064.128.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: 60983475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 578, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.144.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': '144.153', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 153, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6: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: 60983476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 8, 'counter': 579, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.144.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ba1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ba1.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: 60983507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bh1.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: 60983516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bj1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bj1.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: 60983519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 624, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983528
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 625, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.144.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 628, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 629, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60983536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983538
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.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: 60983539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60983545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.144.cm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 60983564
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 6, 'counter': 658, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.156064.192.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': '192.1488', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1488, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/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: 60983565
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 659, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.156064.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.973', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 973, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983567
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 660, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.156064.192.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.973', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 973, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60983568
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 661, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983569
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 662, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983570
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 663, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983571
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983572
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 60983573
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 666, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 60983574
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 667, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983575
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983578
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983579
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.192.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 60983580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 672, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.192.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60983582
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983583
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.192.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: 60983584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 4, 'counter': 676, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.156064.288.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: 60983585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 677, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.156064.288.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': '288.576', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 576, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}.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: 60983586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 685, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 686, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983597
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 689, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60983600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60983620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.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: 60983623
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 60983624
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.288.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 60983625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 60983626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 60983628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 60983630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bh1.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: 60983631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.156064.288.bh1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bh1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983634
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 3, 'counter': 720, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.156064.384.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': '384.18063', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18063, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4.\\GL(2,\\mathbb{Z}/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: 60983635
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.384.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: 60983636
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.384.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: 60983637
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 2, 'counter': 723, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.156064.576.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': '576.8353', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8353, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/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: 60983638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983639
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983641
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983642
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983643
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983645
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 60983646
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983647
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.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: 60983648
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.156064.576.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 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: 60983649
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.156064', 'ambient_counter': 156064, 'ambient_order': 1152, 'ambient_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 1, 'counter': 734, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1152.156064.1152.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': '1152.156064', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6446418664246003612, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6.\\GL(2,\\mathbb{Z}/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: 60982944
    {'ambient': '1152.156064', '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': [5587, 5135, 4560, 5157, 2394, 4065, 3435, 4450], 'generators': [1, 576, 8, 32, 2, 4, 672, 384, 48], 'label': '1152.156064.1.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': '576.8353', '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': '576.8353'}
  • id: 60982945
    {'ambient': '1152.156064', '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.v1.a1', '6.w1.a1', '9.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7953, -1, 2512, -1, 6807, -1, 6451, -1], 'generators': [1, 4, 672, 2, 576, 384, 8, 48], 'label': '1152.156064.3.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': '576.8353', '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: 60982946
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.bl1', '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.f1.a1', '6.g1.a1', '6.w1.a1'], 'contains': ['24.ba1.a1', '24.be1.a1', '24.bg1.a1', '24.dn1.a1', '24.dn1.a2', '36.bg1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7472, -1, 700, -1, 7713, -1, 8613, -1], 'generators': [49, 384, 8, 578, 672, 676], 'label': '1152.156064.12.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': '576.8353', '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': '96.209'}
  • id: 60982947
    {'ambient': '1152.156064', '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': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.k1.a1'], 'contains': ['24.bp1.a1', '24.br1.a1', '24.bt1.a1', '24.dp1.a1', '24.dp1.b1', '36.bh1.a1', '48.v1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1327, -1, 8525, -1, 650, -1, 1598, -1], 'generators': [3, 576, 96, 8, 48, 32], 'label': '1152.156064.12.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': '576.8353', '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': '24.13'}
  • id: 60982948
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.d1.a1', '24.bp1.a1', '24.bx1.a1', '36.bi1.a1', '48.w1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3721, -1, 6116, -1, 1628, -1, 2501, -1], 'generators': [4, 576, 96, 48, 32, 8], 'label': '1152.156064.12.bn1.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.bn1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60982949
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.bo1', '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.i1.a1', '6.l1.a1'], 'contains': ['24.bp1.a1', '24.by1.a1', '24.bz1.a1', '36.bj1.a1', '48.x1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3285, -1, 5003, -1, 1150, -1, 2648, -1], 'generators': [1, 576, 672, 48, 8, 32], 'label': '1152.156064.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '12.bo1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60982950
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '24.l1.a1', '24.q1.a1', '24.bq1.a1', '24.bu1.a1', '24.do1.a1', '24.do1.b1', '24.dq1.a1', '24.dq1.b1', '36.bh1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1527, -1, 8339, -1, 1783, -1, 1944, -1], 'generators': [3, 384, 576, 8, 48, 96], 'label': '1152.156064.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.bp1.a1', 'projective_image': '576.8353', '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': '36.12'}
  • id: 60982951
    {'ambient': '1152.156064', '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.a1.a1', '24.j1.a1', '24.k1.a1', '24.t1.a1', '24.u1.a1', '24.bv1.a1', '24.bw1.a1', '36.bj1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4394, -1, 4309, -1, 3935, -1, 5609, -1], 'generators': [1, 384, 672, 48, 576, 8], 'label': '1152.156064.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.bq1.a1', 'projective_image': '576.8353', '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: 60982952
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.br1', '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.j1.a1', '6.k1.a1'], 'contains': ['24.br1.a1', '24.bt1.a1', '24.bx1.a1', '36.bk1.a1', '48.be1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2515, -1, 7202, -1, 934, -1, 2110, -1], 'generators': [3, 576, 96, 60, 32, 8], 'label': '1152.156064.12.br1.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.br1.a1', 'projective_image': '576.8353', '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': '48.49'}
  • id: 60982953
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.m1.a1', '24.n1.a1', '24.v1.a1', '24.w1.a1', '24.bq1.a1', '24.bu1.a1', '36.bk1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2830, -1, 7047, -1, 2886, -1, 3420, -1], 'generators': [3, 384, 8, 60, 96, 576], 'label': '1152.156064.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.bs1.a1', 'projective_image': '576.8353', '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': '72.48'}
  • id: 60982954
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.s1.a1'], 'contains': ['24.bs1.a1', '24.ca1.a1', '36.a1.a1', '48.bi1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4210, -1, 6295, -1, 4697, -1, 3366, -1], 'generators': [3, 576, 96, 4, 416, 8], 'label': '1152.156064.12.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '12.bt1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60982955
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.k1.a1', '6.t1.a1', '6.u1.a1'], 'contains': ['24.d1.a1', '24.bt1.a1', '36.bl1.a1', '48.bu1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4653, -1, 6050, -1, 1855, -1, 2710, -1], 'generators': [51, 576, 96, 4, 32, 8], 'label': '1152.156064.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bu1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60982956
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '4.a1', '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.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '12.bn1.a1', '16.d1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3984, 8797, 6017, 1996, 1819, 594, 2694, 1210], 'generators': [4, 576, 672, 48, 384, 32, 8], 'label': '1152.156064.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '576.8353', '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': '288.1028'}
  • id: 60982957
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.n1.a1', '6.p1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '24.bb1.a1', '24.bc1.a1', '24.bj1.a1', '24.bv1.a1', '36.bm1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6614, -1, 2403, -1, 5186, -1, 5870, -1], 'generators': [1, 672, 8, 4, 576, 384], 'label': '1152.156064.12.bv1.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.bv1.a1', 'projective_image': '576.8353', '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': '32.46'}
  • id: 60982958
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.bw1', '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': ['4.e1.a1', '6.n1.a1', '6.q1.a1', '6.w1.a1'], 'contains': ['24.b1.a1', '24.bd1.a1', '24.be1.a1', '24.bk1.a1', '24.bw1.a1', '36.bn1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6558, -1, 2315, -1, 5118, -1, 5812, -1], 'generators': [17, 384, 576, 4, 96, 8], 'label': '1152.156064.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bw1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60982959
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.o1.a1', '6.p1.a1', '6.w1.a1'], 'contains': ['24.b1.a1', '24.bf1.a1', '24.bg1.a1', '36.bo1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9157, -1, 1306, -1, 6613, -1, 7864, -1], 'generators': [2, 8, 672, 576, 384, 4], 'label': '1152.156064.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bx1.a1', 'projective_image': '576.8353', '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': '16.14'}
  • id: 60982960
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.o1.a1', '6.q1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '24.bh1.a1', '24.bi1.a1', '36.bp1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9098, -1, 1449, -1, 6541, -1, 7472, -1], 'generators': [18, 384, 8, 96, 4, 576], 'label': '1152.156064.12.by1.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.by1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60982961
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.bz1', '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.n1.a1'], 'contains': ['24.c1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1', '24.bo1.a1', '24.bv1.a1', '24.bw1.a1', '36.bq1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4836, -1, 4098, -1, 4089, -1, 5670, -1], 'generators': [1, 384, 672, 60, 576, 8], 'label': '1152.156064.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.bz1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60982962
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.l1.a1', '6.r1.a1', '6.u1.a1'], 'contains': ['24.d1.a1', '24.bz1.a1', '36.bn1.a1', '48.cj1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4603, -1, 4610, -1, 2194, -1, 2976, -1], 'generators': [17, 576, 672, 4, 8, 32], 'label': '1152.156064.12.ca1.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.ca1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60982963
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.m1.a1', '6.r1.a1', '6.t1.a1'], 'contains': ['24.d1.a1', '36.bp1.a1', '48.cl1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6919, -1, 4195, -1, 2555, -1, 4357, -1], 'generators': [18, 576, 672, 4, 8, 32], 'label': '1152.156064.12.cb1.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.cb1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60982964
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.cc1', '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.k1.a1', '6.l1.a1'], 'contains': ['24.bx1.a1', '24.by1.a1', '24.bz1.a1', '36.bq1.a1', '48.cm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3243, -1, 5140, -1, 1216, -1, 2804, -1], 'generators': [1, 576, 672, 60, 8, 32], 'label': '1152.156064.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '12.cc1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60982965
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, '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.s1.a1'], 'contains': ['24.ca1.a1', '24.cb1.a1', '36.bn1.a1', '48.cn1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5042, -1, 4358, -1, 4742, -1, 3663, -1], 'generators': [17, 576, 672, 4, 8, 416], 'label': '1152.156064.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.cd1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60982966
    {'ambient': '1152.156064', '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.s1.a1'], 'contains': ['24.ca1.a1', '36.bp1.a1', '48.co1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6950, -1, 3967, -1, 4914, -1, 4673, -1], 'generators': [18, 576, 672, 4, 8, 416], 'label': '1152.156064.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.ce1.a1', 'projective_image': '576.8353', '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: 60982967
    {'ambient': '1152.156064', '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.d1.a1', '12.b1.a1', '12.c1.a1', '12.bt1.a1', '16.g1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4273, 1578, 6085, 8634, 2182, 7954, 3208, 8086], 'generators': [3, 672, 8, 4, 576, 32, 384], 'label': '1152.156064.4.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', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '576.8353', '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': '192.1488'}
  • id: 60982968
    {'ambient': '1152.156064', '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': '288.d1.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.cr1.a1', '24.cs1.a1', '24.dg1.a1', '24.dh1.a1', '36.br1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5208, -1, 4563, -1, 2261, -1, 3239, -1], 'generators': [1, 32, 8, 2, 48, 4], 'label': '1152.156064.12.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': '576.8353', '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': '24.8'}
  • id: 60982969
    {'ambient': '1152.156064', '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.d1.a1'], 'contains': ['24.e1.a1', '24.ci1.a1', '24.cj1.a1', '24.cp1.a1', '24.cq1.a1', '24.di1.a1', '24.dj1.a1', '36.br1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8953, -1, 1890, -1, 9126, -1, 7252, -1], 'generators': [1, 384, 8, 2, 48, 4], 'label': '1152.156064.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cg1.a1', 'projective_image': '576.8353', '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: 60982970
    {'ambient': '1152.156064', '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.d1.a1'], 'contains': ['24.cg1.a1', '24.ci1.a1', '24.cj1.a1', '24.dc1.a1', '24.dd1.a1', '24.dk1.a1', '24.dl1.a1', '36.bs1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7664, -1, 1829, -1, 9696, -1, 7796, -1], 'generators': [1, 384, 8, 674, 48, 4], 'label': '1152.156064.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.ch1.a1', 'projective_image': '576.8353', '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: 60982971
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.ch1.a1', '24.ck1.a1', '24.cl1.a1', '24.de1.a1', '24.df1.a1', '24.dm1.a1', '24.dn1.a1', '36.bt1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6819, -1, 896, -1, 8595, -1, 9409, -1], 'generators': [1, 384, 8, 578, 48, 676], 'label': '1152.156064.12.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.ci1.a1', 'projective_image': '576.8353', '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: 60982972
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.ch1.a2', '24.ck1.a1', '24.cl1.a1', '24.de1.a2', '24.df1.a2', '24.dm1.a2', '24.dn1.a2', '36.bt1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6819, -1, 956, -1, 8595, -1, 9335, -1], 'generators': [1, 384, 8, 98, 48, 676], 'label': '1152.156064.12.ci1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.ci1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60982973
    {'ambient': '1152.156064', '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.d1.a1'], 'contains': ['24.co1.a1', '24.cp1.a1', '24.cq1.a1', '24.cy1.a1', '24.cz1.a1', '24.dk1.a1', '24.dl1.a1', '36.bu1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8813, -1, 1769, -1, 9309, -1, 7723, -1], 'generators': [1, 384, 8, 2, 720, 4], 'label': '1152.156064.12.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cj1.a1', 'projective_image': '576.8353', '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: 60982974
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.ck1', '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.d1.a1'], 'contains': ['24.cv1.a1', '24.cy1.a1', '24.cz1.a1', '24.dc1.a1', '24.dd1.a1', '24.di1.a1', '24.dj1.a1', '36.bv1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8399, -1, 1950, -1, 9528, -1, 7594, -1], 'generators': [1, 384, 8, 674, 720, 4], 'label': '1152.156064.12.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.ck1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60982975
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '12.cl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.cx1.a1', '24.da1.a1', '24.db1.a1', '24.de1.a1', '24.df1.a1', '24.dm1.a2', '24.dn1.a2', '36.bw1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6746, -1, 1016, -1, 8681, -1, 9262, -1], 'generators': [1, 384, 8, 578, 720, 676], 'label': '1152.156064.12.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.cl1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60982976
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '12.cl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.cx1.a2', '24.da1.a1', '24.db1.a1', '24.de1.a2', '24.df1.a2', '24.dm1.a1', '24.dn1.a1', '36.bw1.a2'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6746, -1, 836, -1, 8681, -1, 9482, -1], 'generators': [1, 384, 8, 98, 720, 676], 'label': '1152.156064.12.cl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.cl1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cl1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60982977
    {'ambient': '1152.156064', '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.d1.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.u1.a1', '64.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1200, 8179, 8279, 2696, 722, 2205, 1790, 2909], 'generators': [8, 576, 32, 384, 672], 'label': '1152.156064.16.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': '576.8353', '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: 60982978
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '4.c1', '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.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '12.d1.a1', '12.bu1.a1', '16.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4693, 3064, 5830, 6264, 1995, 6025, 2824, 6283], 'generators': [51, 576, 672, 4, 384, 32, 8], 'label': '1152.156064.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8353'}
  • id: 60982979
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '144.b1.a1', 'complements': ['72.cc1.a1', '72.co1.a2', '72.co1.a1', '72.cm1.a1', '72.cr1.a1', '72.cv1.a2', '72.cv1.a1', '72.ct1.a1', '72.cq1.a1', '72.cu1.a1', '72.cs1.a1', '72.cu1.a2', '72.cd1.a1', '72.cp1.a1', '72.cn1.a1', '72.cp1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '48.f1.a1', '48.cw1.a1', '64.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [138, 9068, 9435, 840, 300, 1365, 399, 1216], 'generators': [48, 384, 32, 672, 576], 'label': '1152.156064.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60982996
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.f1.a1', '36.g1.a1', '36.m1.a1', '36.o1.a1', '36.ba1.a1', '36.bc1.a1', '36.br1.a1', '36.bs1.a1', '36.bu1.a1', '36.bv1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9581, -1, 726, -1, 8050, -1, 8226, -1], 'generators': [1, 2, 48, 672], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60982980
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '144.b1.a1', 'complements': ['72.cc1.a1', '72.co1.a2', '72.co1.a1', '72.cm1.a1', '72.cr1.a1', '72.cv1.a2', '72.cv1.a1', '72.ct1.a1', '72.cq1.a1', '72.cu1.a1', '72.cs1.a1', '72.cu1.a2', '72.cd1.a1', '72.cp1.a1', '72.cn1.a1', '72.cp1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.f1.b1', '48.cw1.b1', '64.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [138, 9068, 9504, 1651, 300, 1365, 456, 436], 'generators': [56, 384, 32, 672, 576], 'label': '1152.156064.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '1152.156064', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60982981
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '96.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '32.i1.a1', '32.i1.b1', '48.v1.a1', '48.y1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 8069, -1, 790, -1, 1399, -1], 'generators': [3, 384, 8, 48, 32], 'label': '1152.156064.16.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': '576.8353', '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': '12.4'}
  • id: 60982982
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '96.t1.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.e1.a1', '32.f1.a1', '48.c1.a1', '48.w1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3767, -1, 6495, -1, 1507, -1, 2468, -1], 'generators': [4, 384, 48, 32, 8], 'label': '1152.156064.16.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': '576.8353', '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': '24.14'}
  • id: 60982983
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '16.e1', '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.i1.a1'], 'contains': ['32.b1.a1', '32.g1.a1', '32.h1.a1', '48.x1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3563, -1, 5061, -1, 1176, -1, 2634, -1], 'generators': [1, 384, 48, 8, 32], 'label': '1152.156064.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '16.e1.a1', 'projective_image': '576.8353', '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': '72.46'}
  • id: 60982984
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '192.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '8.h1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.f1.a1', '48.be1.a1', '48.bf1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1834, -1, 7655, -1, 994, -1, 2076, -1], 'generators': [3, 384, 60, 32, 8], 'label': '1152.156064.16.f1.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.f1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60982985
    {'ambient': '1152.156064', 'aut_centralizer_order': 36, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '64.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.e1.a1', '48.d1.a1', '48.bh1.a1', '48.bi1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4110, -1, 7009, -1, 2201, -1, 3117, -1], 'generators': [3, 8, 4, 32, 384], 'label': '1152.156064.16.g1.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.g1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60982986
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.h1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '48.e1.a1', '48.bu1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4761, -1, 6378, -1, 1988, -1, 2689, -1], 'generators': [51, 384, 4, 32, 8], 'label': '1152.156064.16.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': '576.8353', '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: 60982987
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '16.i1', '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.d1.a1', '8.i1.a1', '8.k1.a1', '8.m1.a1'], 'contains': ['32.e1.a1', '32.g1.a1', '48.by1.a1', '48.ci1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4966, -1, 5519, -1, 2053, -1, 3050, -1], 'generators': [1, 32, 4, 384, 8], 'label': '1152.156064.16.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': '576.8353', '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': '48.43'}
  • id: 60982988
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.958', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.i1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.h1.a1', '48.bz1.a1', '48.cj1.a1', '48.cn1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4819, -1, 4549, -1, 2408, -1, 3194, -1], 'generators': [17, 384, 4, 8, 32], 'label': '1152.156064.16.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': '576.8353', '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': '144.153'}
  • id: 60982989
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': ['288.w1.a1', '288.x1.a1', '288.bf1.a1', '288.bg1.a1', '288.bh1.a2', '288.bh1.a1', '288.w1.b1', '288.x1.b1', '288.bf1.b1', '288.bg1.b1', '288.bh1.b2', '288.bh1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '12.e1.a1', '12.bv1.a1', '16.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4926, 4149, 5631, 5265, 2060, 3960, 3145, 5323], 'generators': [1, 672, 32, 4, 576, 384, 8], 'label': '1152.156064.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '576.8353', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 60982990
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.j1.a1', '8.k1.a1', '8.n1.a1'], 'contains': ['32.e1.a1', '48.ca1.a1', '48.ck1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7101, -1, 3926, -1, 2628, -1, 4490, -1], 'generators': [2, 32, 384, 4, 8], 'label': '1152.156064.16.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': '576.8353', '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': '24.14'}
  • id: 60982991
    {'ambient': '1152.156064', '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.j1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.e1.a1', '48.cb1.a1', '48.cl1.a1', '48.co1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7030, -1, 4078, -1, 2991, -1, 4443, -1], 'generators': [18, 384, 4, 8, 32], 'label': '1152.156064.16.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': '576.8353', '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: 60982992
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '16.m1', '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.i1.a1'], 'contains': ['32.f1.a1', '32.g1.a1', '32.h1.a1', '48.cg1.a1', '48.cm1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3504, -1, 5326, -1, 1246, -1, 2735, -1], 'generators': [1, 384, 60, 8, 32], 'label': '1152.156064.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '16.m1.a1', 'projective_image': '576.8353', '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': '72.46'}
  • id: 60982993
    {'ambient': '1152.156064', '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': '96.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.cx1.a1', '48.cy1.a1', '48.cz1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [47, -1, 9936, -1, 232, -1, 193, -1], 'generators': [3, 576, 32, 384, 672], 'label': '1152.156064.16.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': '1152.156064', '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': '24.13'}
  • id: 60982994
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '288.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.da1.a1', '48.db1.a1', '64.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [398, -1, 9775, -1, 118, -1, 355, -1], 'generators': [51, 384, 32, 672, 576], 'label': '1152.156064.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.o1.a1', 'projective_image': '1152.156064', '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': '72.44'}
  • id: 60982995
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.e1.a1', '36.h1.a1', '36.l1.a1', '36.n1.a1', '36.z1.a1', '36.bb1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8059, -1, 3223, -1, 5937, -1, 6602, -1], 'generators': [577, 578, 48], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60982997
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.g1.a1', '36.v1.a1', '36.x1.a1', '36.bd1.a1', '36.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7771, -1, 3147, -1, 6242, -1, 6657, -1], 'generators': [577, 2, 48], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60982998
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.f1.a1', '36.h1.a1', '36.w1.a1', '36.y1.a1', '36.be1.a1', '36.bg1.a1', '36.bt1.a1', '36.bt1.a2', '36.bw1.a1', '36.bw1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8964, -1, 327, -1, 7386, -1, 8978, -1], 'generators': [1, 578, 48, 672], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60982999
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.k1.a1', '36.l1.a1', '36.o1.a1', '36.q1.a1', '36.t1.a1', '36.bd1.a1', '36.bg1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8334, -1, 2762, -1, 6689, -1, 6851, -1], 'generators': [577, 578, 624], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983000
    {'ambient': '1152.156064', '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.w1.a1', '288.x1.a1', '288.bg1.a1', '288.bf1.a1', '288.bh1.a1', '288.bh1.a2', '288.w1.b1', '288.x1.b1', '288.bg1.b1', '288.bf1.b1', '288.bh1.b1', '288.bh1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '12.bw1.a1', '12.ca1.a1', '12.cd1.a1', '16.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4781, 6430, 4490, 4226, 2351, 2890, 3272, 2333], 'generators': [17, 672, 384, 4, 576, 8, 32], 'label': '1152.156064.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '576.8353', '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': '576.8353'}
  • id: 60983001
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.k1.a1', '36.m1.a1', '36.n1.a1', '36.r1.a1', '36.s1.a1', '36.be1.a1', '36.bf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7909, -1, 2453, -1, 6170, -1, 7116, -1], 'generators': [1, 2, 624], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983002
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.q1.a1', '36.s1.a1', '36.v1.a1', '36.y1.a1', '36.z1.a1', '36.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8692, -1, 2816, -1, 6467, -1, 6983, -1], 'generators': [577, 2, 624], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983003
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.r1.a1', '36.t1.a1', '36.w1.a1', '36.x1.a1', '36.ba1.a1', '36.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8194, -1, 2573, -1, 6389, -1, 7182, -1], 'generators': [1, 578, 624], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983004
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.k1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.j1.a1', '36.k1.a1', '36.p1.a1', '36.bh1.a1', '36.bi1.a1', '36.bk1.a1', '36.bl1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4078, -1, 5878, -1, 4791, -1, 4315, -1], 'generators': [3, 4, 48, 576, 96], 'label': '1152.156064.18.i1.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.i1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983005
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.n1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '36.i1.a1', '36.q1.a1', '36.r1.a1', '36.u1.a1', '36.bi1.a1', '36.bj1.a1', '36.bm1.a1', '36.bn1.a1', '36.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7296, -1, 3459, -1, 4859, -1, 6073, -1], 'generators': [1, 4, 48, 576], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983006
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '6.o1.a1', '9.a1.a1'], 'contains': ['36.g1.a1', '36.h1.a1', '36.s1.a1', '36.t1.a1', '36.bi1.a1', '36.bo1.a1', '36.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9823, -1, 1255, -1, 6312, -1, 8133, -1], 'generators': [2, 48, 576], 'label': '1152.156064.18.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.k1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983007
    {'ambient': '1152.156064', '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': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.l1.a1', '36.m1.a1', '36.v1.a1', '36.w1.a1', '36.bm1.a1', '36.bo1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8487, -1, 2377, -1, 6092, -1, 6917, -1], 'generators': [1, 2, 576], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983008
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.r1.a1', '6.s1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.n1.a1', '36.o1.a1', '36.x1.a1', '36.y1.a1', '36.bn1.a1', '36.bp1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7844, -1, 2324, -1, 5865, -1, 6718, -1], 'generators': [17, 18, 96], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983009
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.v1.a1', '9.a1.a1'], 'contains': ['36.z1.a1', '36.ba1.a1', '36.bd1.a1', '36.be1.a1', '36.bl1.a1', '36.bm1.a1', '36.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8602, -1, 2507, -1, 5709, -1, 6785, -1], 'generators': [65, 18, 96], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983010
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.w1.a1', '9.a1.a1'], 'contains': ['36.bb1.a1', '36.bc1.a1', '36.bf1.a1', '36.bg1.a1', '36.bl1.a1', '36.bn1.a1', '36.bo1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7987, -1, 2238, -1, 5787, -1, 7050, -1], 'generators': [49, 2, 576], 'label': '1152.156064.18.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': '576.8353', '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': '16.11'}
  • id: 60983011
    {'ambient': '1152.156064', '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': '96.b1.a1', 'complements': ['288.w1.a1', '288.x1.a1', '288.bf1.a1', '288.bg1.a1', '288.bh1.a2', '288.bh1.a1', '288.w1.b1', '288.x1.b1', '288.bf1.b1', '288.bg1.b1', '288.bh1.b2', '288.bh1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.f1.a1', '12.bx1.a1', '16.k1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6995, 7561, 3943, 7261, 2694, 4999, 4456, 4351], 'generators': [2, 672, 32, 384, 576, 4, 8], 'label': '1152.156064.4.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.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '576.8353', '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': '96.226'}
  • id: 60983012
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.f1.b1', '48.g1.a1', '48.i1.a1', '48.cp1.a1', '48.cp1.b1', '72.bl1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1499, 7337, 8227, 2673, 1725, 3114, 1918, 2059], 'generators': [8, 384, 48, 96, 576], 'label': '1152.156064.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '48.f1.b1', '48.f1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60983013
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.d1.a1', '12.bv1.a1', '12.bw1.a1', '12.bx1.a1', '12.by1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '48.n1.a1', '72.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6394, 4090, 2811, 5315, 5072, 6423, 5595, 5945], 'generators': [4, 8, 96, 576, 384], 'label': '1152.156064.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.d1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '576.8353', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60983014
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.bs1.a1', '12.bz1.a1'], 'contains': ['48.a1.a1', '48.o1.a1', '48.p1.a1', '72.bo1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4034, 6207, 4073, 3960, 3050, 4184, 4823, 3851], 'generators': [60, 384, 96, 576, 8], 'label': '1152.156064.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60983015
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '24.d1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1', '12.bn1.a1', '12.bu1.a1', '12.ca1.a1', '12.cb1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '96.t1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4563, 5141, 6417, 6656, 1914, 5191, 2815, 5014], 'generators': [4, 576, 32, 8, 96], 'label': '1152.156064.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60983016
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.h1.a1', '12.cg1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '48.y1.a1', '48.bf1.a1', '72.bs1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4323, 1275, 6783, 7479, 6471, 8638, 4135, 8016], 'generators': [3, 384, 4, 48, 8], 'label': '1152.156064.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.e1.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.e1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983017
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.bp1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.k1.a1', '48.y1.a1', '48.z1.a1', '48.bc1.a1', '48.bj1.a1', '48.cq1.a1', '48.cq1.b1', '48.dc1.a1', '48.dc1.b1', '72.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2014, -1, 7625, -1, 2876, -1, 2304, -1], 'generators': [3, 384, 8, 48, 96], 'label': '1152.156064.24.f1.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.f1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983018
    {'ambient': '1152.156064', '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': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.bp1.a1'], 'contains': ['48.g1.a1', '48.j1.a1', '48.l1.a1', '48.z1.a1', '48.bk1.a1', '48.bk1.a2', '48.cr1.a1', '48.cr1.b1', '48.dd1.a1', '48.dd1.b1', '72.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2263, -1, 7292, -1, 2753, -1, 2415, -1], 'generators': [579, 384, 8, 48, 96], 'label': '1152.156064.24.g1.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.g1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983019
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.m1.a1', '48.o1.a1', '48.ba1.a1', '48.bl1.a1', '48.bm1.a1', '72.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6292, -1, 3331, -1, 6295, -1, 5909, -1], 'generators': [4, 384, 48, 96, 8], 'label': '1152.156064.24.h1.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.h1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983020
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.n1.a1'], 'contains': ['48.g1.a1', '48.n1.a1', '48.p1.a1', '48.ba1.a1', '48.bn1.a1', '72.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5305, -1, 3757, -1, 3970, -1, 5269, -1], 'generators': [580, 384, 48, 96, 8], 'label': '1152.156064.24.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': '576.8353', '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': '24.14'}
  • id: 60983021
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.n1.a1', '12.bq1.a1'], 'contains': ['48.g1.a1', '48.q1.a1', '48.s1.a1', '48.de1.a1', '48.de1.b1', '72.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3291, -1, 5076, -1, 4135, -1, 5839, -1], 'generators': [577, 384, 48, 672, 680], 'label': '1152.156064.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.j1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983022
    {'ambient': '1152.156064', '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.w1.a1', '288.x1.a1', '288.bg1.a1', '288.bf1.a1', '288.bh1.a1', '288.bh1.a2', '288.w1.b1', '288.x1.b1', '288.bg1.b1', '288.bf1.b1', '288.bh1.b1', '288.bh1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.by1.a1', '12.cb1.a1', '12.ce1.a1', '16.l1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6793, 5273, 4039, 3162, 2776, 1795, 4386, 3357], 'generators': [18, 672, 384, 4, 576, 8, 32], 'label': '1152.156064.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '576.8353', '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: 60983023
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.n1.a1', '12.bq1.a1'], 'contains': ['48.g1.a1', '48.r1.a1', '48.t1.a1', '48.bb1.a1', '48.bo1.a1', '72.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5613, -1, 2351, -1, 4737, -1, 6648, -1], 'generators': [1, 384, 48, 672, 8], 'label': '1152.156064.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.k1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983024
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.p1.a1', '12.bp1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.l1.a1', '48.bc1.a1', '48.bk1.a1', '48.bk1.a2', '48.cu1.a1', '48.cu1.b1', '48.df1.a1', '48.df1.a2', '72.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1902, -1, 7583, -1, 2692, -1, 2200, -1], 'generators': [3, 384, 8, 624, 96], 'label': '1152.156064.24.l1.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.l1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983025
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.m1', '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': ['12.h1.a1', '12.o1.a1', '12.bs1.a1'], 'contains': ['48.h1.a1', '48.k1.a1', '48.o1.a1', '48.bf1.a1', '48.bg1.a1', '48.bp1.a1', '48.bq1.a1', '72.i1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2500, -1, 7174, -1, 3354, -1, 3482, -1], 'generators': [3, 384, 60, 96, 8], 'label': '1152.156064.24.m1.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.m1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983026
    {'ambient': '1152.156064', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.p1.a1', '12.bs1.a1'], 'contains': ['48.h1.a1', '48.l1.a1', '48.p1.a1', '48.bg1.a1', '48.br1.a1', '48.br1.a2', '72.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2807, -1, 6145, -1, 3120, -1, 3537, -1], 'generators': [3, 384, 636, 96, 8], 'label': '1152.156064.24.n1.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.n1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983027
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.g1.a1', '12.o1.a1'], 'contains': ['48.h1.a1', '48.j1.a1', '48.n1.a1', '48.bd1.a1', '48.bt1.a1', '48.bt1.a2', '72.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2961, -1, 6094, -1, 3750, -1, 4281, -1], 'generators': [3, 8, 580, 96, 384], 'label': '1152.156064.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983028
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.h1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.m1.a1', '48.bd1.a1', '48.bs1.a1', '72.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4461, -1, 6379, -1, 6859, -1, 4930, -1], 'generators': [3, 8, 4, 96, 384], 'label': '1152.156064.24.p1.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': '24.p1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60983029
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.u1.a1', '12.bp1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '48.k1.a1', '48.bj1.a1', '48.bk1.a1', '48.bk1.a2', '48.cv1.a1', '48.cv1.b1', '48.dg1.a1', '48.dg1.a2', '72.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2077, -1, 7530, -1, 2815, -1, 2252, -1], 'generators': [579, 384, 8, 624, 96], 'label': '1152.156064.24.q1.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.q1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983030
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.p1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1'], 'contains': ['48.i1.a1', '48.m1.a1', '48.p1.a1', '48.bl1.a1', '48.bn1.a1', '72.n1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6178, -1, 3625, -1, 5581, -1, 5723, -1], 'generators': [4, 384, 624, 96, 8], 'label': '1152.156064.24.r1.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.r1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983031
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.o1.a1', '12.z1.a1'], 'contains': ['48.i1.a1', '48.n1.a1', '48.o1.a1', '48.bm1.a1', '48.bn1.a1', '72.o1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5373, -1, 3544, -1, 4053, -1, 5339, -1], 'generators': [580, 384, 624, 96, 8], 'label': '1152.156064.24.s1.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.s1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983032
    {'ambient': '1152.156064', '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.v1.a1', '12.z1.a1', '12.bq1.a1'], 'contains': ['48.i1.a1', '48.q1.a1', '48.t1.a1', '72.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4818, -1, 4591, -1, 4303, -1, 6052, -1], 'generators': [577, 384, 624, 680, 672], 'label': '1152.156064.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.t1.a1', 'projective_image': '576.8353', '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: 60983033
    {'ambient': '1152.156064', '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': '288.e1.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.b1', '12.bm1.a1', '12.bp1.a1', '16.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1380, -1, 8339, -1, 763, -1, 1701, -1], 'generators': [3, 576, 672, 8, 384, 48, 32], 'label': '1152.156064.4.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': '576.8353', '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': '144.190'}
  • id: 60983034
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.u1', '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.w1.a1', '12.z1.a1', '12.bq1.a1'], 'contains': ['48.i1.a1', '48.r1.a1', '48.s1.a1', '72.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4373, -1, 4190, -1, 4231, -1, 6121, -1], 'generators': [1, 384, 624, 8, 672], 'label': '1152.156064.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.u1.a1', 'projective_image': '576.8353', '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: 60983035
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.v1', '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.g1.a1', '12.u1.a1', '12.bs1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.p1.a1', '48.bp1.a1', '48.br1.a1', '48.br1.a2', '72.r1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2437, -1, 6897, -1, 3186, -1, 3593, -1], 'generators': [579, 384, 636, 96, 8], 'label': '1152.156064.24.v1.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.v1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983036
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.w1', '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.i1.a1', '12.o1.a1', '12.bs1.a1'], 'contains': ['48.j1.a1', '48.l1.a1', '48.o1.a1', '48.bq1.a1', '48.br1.a1', '48.br1.a2', '72.s1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2633, -1, 6244, -1, 3288, -1, 3785, -1], 'generators': [579, 384, 60, 96, 8], 'label': '1152.156064.24.w1.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.w1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983037
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.i1.a1', '12.u1.a1', '12.ba1.a1', '12.bb1.a1', '12.bc1.a1', '12.bd1.a1'], 'contains': ['48.j1.a1', '48.m1.a1', '48.bs1.a1', '48.bt1.a1', '48.bt1.a2', '72.t1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6501, -1, 4559, -1, 6805, -1, 5781, -1], 'generators': [579, 8, 4, 96, 384], 'label': '1152.156064.24.x1.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': '24.x1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60983038
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.y1', '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.g1.a1', '12.o1.a1'], 'contains': ['48.k1.a1', '48.l1.a1', '48.n1.a1', '48.bv1.a1', '48.bx1.a1', '48.bx1.a2', '72.u1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3129, -1, 4425, -1, 3691, -1, 4231, -1], 'generators': [51, 384, 580, 96, 8], 'label': '1152.156064.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983039
    {'ambient': '1152.156064', '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.h1.a1', '12.u1.a1', '12.be1.a1', '12.bf1.a1', '12.bg1.a1', '12.bh1.a1'], 'contains': ['48.e1.a1', '48.k1.a1', '48.m1.a1', '48.bv1.a1', '48.bw1.a1', '72.v1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5434, -1, 5388, -1, 6918, -1, 4980, -1], 'generators': [51, 384, 4, 96, 8], 'label': '1152.156064.24.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': '576.8353', '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: 60983040
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', '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.i1.a1', '12.p1.a1', '12.bi1.a1', '12.bj1.a1', '12.bk1.a1', '12.bl1.a1'], 'contains': ['48.l1.a1', '48.m1.a1', '48.bw1.a1', '48.bx1.a1', '48.bx1.a2', '72.w1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6451, -1, 3706, -1, 6629, -1, 5401, -1], 'generators': [627, 384, 4, 96, 8], 'label': '1152.156064.24.ba1.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.ba1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983041
    {'ambient': '1152.156064', '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.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.q1.a1', '12.v1.a1', '12.ba1.a1', '12.be1.a1', '12.bi1.a1', '12.bv1.a1'], 'contains': ['48.m1.a1', '48.q1.a1', '72.x1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7091, -1, 3238, -1, 6221, -1, 6452, -1], 'generators': [577, 672, 4, 384, 680], 'label': '1152.156064.24.bb1.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.bb1.a1', 'projective_image': '576.8353', '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: 60983042
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.r1.a1', '12.w1.a1', '12.bb1.a1', '12.bf1.a1', '12.bj1.a1', '12.bv1.a1'], 'contains': ['48.m1.a1', '48.r1.a1', '48.by1.a1', '48.cc1.a1', '72.y1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6985, -1, 2282, -1, 7739, -1, 8040, -1], 'generators': [1, 8, 4, 672, 384], 'label': '1152.156064.24.bc1.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.bc1.a1', 'projective_image': '576.8353', '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': '32.46'}
  • id: 60983043
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, '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.s1.a1', '12.w1.a1', '12.bc1.a1', '12.bg1.a1', '12.bk1.a1', '12.bw1.a1'], 'contains': ['48.m1.a1', '48.s1.a1', '72.z1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6771, -1, 2854, -1, 6092, -1, 6537, -1], 'generators': [113, 384, 4, 584, 576], 'label': '1152.156064.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bd1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983044
    {'ambient': '1152.156064', '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.b1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '12.bo1.a1', '12.bq1.a1', '16.e1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3543, -1, 5020, -1, 1189, -1, 2770, -1], 'generators': [1, 672, 384, 48, 576, 8, 32], 'label': '1152.156064.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '576.8353', '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: 60983045
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.t1.a1', '12.v1.a1', '12.bd1.a1', '12.bh1.a1', '12.bl1.a1', '12.bw1.a1'], 'contains': ['48.m1.a1', '48.t1.a1', '48.bz1.a1', '48.cd1.a1', '72.ba1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7035, -1, 1582, -1, 7799, -1, 7570, -1], 'generators': [17, 384, 4, 576, 8], 'label': '1152.156064.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983046
    {'ambient': '1152.156064', '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': '24.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.r1.a1', '12.x1.a1', '12.ba1.a1', '12.bh1.a1', '12.bk1.a1', '12.bx1.a1'], 'contains': ['48.m1.a1', '48.ca1.a1', '72.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9387, -1, 1319, -1, 8272, -1, 7485, -1], 'generators': [2, 8, 672, 384, 4], 'label': '1152.156064.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bf1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983047
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.q1.a1', '12.y1.a1', '12.bb1.a1', '12.bg1.a1', '12.bl1.a1', '12.bx1.a1'], 'contains': ['48.m1.a1', '48.ce1.a1', '72.bc1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8211, -1, 511, -1, 7617, -1, 8714, -1], 'generators': [578, 8, 672, 384, 676], 'label': '1152.156064.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bg1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60983048
    {'ambient': '1152.156064', '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': '72.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.s1.a1', '12.x1.a1', '12.bd1.a1', '12.be1.a1', '12.bj1.a1', '12.by1.a1'], 'contains': ['48.m1.a1', '48.cf1.a1', '72.bd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8913, -1, 988, -1, 7553, -1, 8659, -1], 'generators': [114, 384, 576, 580, 8], 'label': '1152.156064.24.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': '576.8353', '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': '24.14'}
  • id: 60983049
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.t1.a1', '12.y1.a1', '12.bc1.a1', '12.bf1.a1', '12.bi1.a1', '12.by1.a1'], 'contains': ['48.m1.a1', '48.cb1.a1', '72.be1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9259, -1, 2153, -1, 8338, -1, 7253, -1], 'generators': [18, 384, 576, 4, 8], 'label': '1152.156064.24.bi1.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.bi1.a1', 'projective_image': '576.8353', '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: 60983050
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.z1.a1', '12.bv1.a1'], 'contains': ['48.n1.a1', '48.q1.a1', '48.r1.a1', '72.bf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6092, -1, 2593, -1, 4552, -1, 6266, -1], 'generators': [1, 672, 580, 384, 8], 'label': '1152.156064.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bj1.a1', 'projective_image': '576.8353', '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': '16.14'}
  • id: 60983051
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.bk1', '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.n1.a1', '12.z1.a1', '12.bw1.a1'], 'contains': ['48.n1.a1', '48.s1.a1', '48.t1.a1', '72.bg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5842, -1, 2711, -1, 4501, -1, 6192, -1], 'generators': [17, 384, 100, 8, 576], 'label': '1152.156064.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bk1.a1', 'projective_image': '576.8353', '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: 60983052
    {'ambient': '1152.156064', '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': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.z1.a1', '12.bz1.a1'], 'contains': ['48.o1.a1', '48.q1.a1', '48.s1.a1', '72.bh1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3405, -1, 4481, -1, 4194, -1, 5959, -1], 'generators': [577, 384, 60, 680, 672], 'label': '1152.156064.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bl1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983053
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.bm1', '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.k1.a1', '12.z1.a1', '12.bz1.a1'], 'contains': ['48.o1.a1', '48.r1.a1', '48.t1.a1', '48.cg1.a1', '48.ch1.a1', '72.bi1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5551, -1, 2402, -1, 4811, -1, 6711, -1], 'generators': [1, 384, 60, 672, 8], 'label': '1152.156064.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bm1.a1', 'projective_image': '576.8353', '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: 60983054
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', '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.n1.a1', '12.v1.a1', '12.bz1.a1'], 'contains': ['48.p1.a1', '48.q1.a1', '48.t1.a1', '72.bj1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4903, -1, 3834, -1, 4344, -1, 6157, -1], 'generators': [577, 384, 636, 680, 672], 'label': '1152.156064.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bn1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983055
    {'ambient': '1152.156064', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.j1.a1', '6.a1.a1', '6.k1.a1', '8.h1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4078, 1755, 6085, 7400, 1867, 7431, 2736, 7440], 'generators': [3, 8, 672, 4, 32, 384, 576, 48], 'label': '1152.156064.2.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.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8353'}
  • id: 60983056
    {'ambient': '1152.156064', '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.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '12.br1.a1', '12.bs1.a1', '16.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2515, -1, 7193, -1, 980, -1, 2110, -1], 'generators': [3, 576, 672, 60, 384, 32, 8], 'label': '1152.156064.4.j1.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.j1.a1', 'projective_image': '576.8353', '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': '288.1037'}
  • id: 60983057
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.bo1', '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.n1.a1', '12.w1.a1', '12.bz1.a1'], 'contains': ['48.p1.a1', '48.r1.a1', '48.s1.a1', '72.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5255, -1, 3863, -1, 4267, -1, 6222, -1], 'generators': [1, 384, 636, 8, 672], 'label': '1152.156064.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bo1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983058
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.b1.a1', '48.cw1.a1', '48.cw1.b1', '72.bl1.a1', '96.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1022, -1, 8503, -1, 650, -1, 888, -1], 'generators': [8, 576, 48, 32, 96], 'label': '1152.156064.24.bp1.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.bp1.a1', 'projective_image': '576.8353', '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': '24.12'}
  • id: 60983059
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.b1.a1', '12.bp1.a1', '12.bs1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.j1.a1', '48.cs1.a1', '48.cx1.a1', '72.bm1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1444, -1, 8345, -1, 1631, -1, 1970, -1], 'generators': [3, 384, 8, 96, 576], 'label': '1152.156064.24.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': '576.8353', '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': '12.5'}
  • id: 60983060
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1', '12.bm1.a1', '12.br1.a1'], 'contains': ['48.b1.a1', '48.cy1.a1', '72.bm1.a1', '96.i1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1187, -1, 8599, -1, 574, -1, 1728, -1], 'generators': [3, 576, 8, 32, 96], 'label': '1152.156064.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.br1.a1', 'projective_image': '576.8353', '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': '24.13'}
  • id: 60983061
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bt1.a1'], 'contains': ['48.u1.a1', '48.cz1.a1', '72.bm1.a1', '96.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1072, -1, 8440, -1, 1375, -1, 1838, -1], 'generators': [3, 576, 8, 416, 96], 'label': '1152.156064.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.bs1.a1', 'projective_image': '576.8353', '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': '24.13'}
  • id: 60983062
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bm1.a1', '12.br1.a1', '12.bu1.a1'], 'contains': ['48.b1.a1', '48.da1.a1', '72.bn1.a1', '96.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1136, -1, 8398, -1, 497, -1, 1642, -1], 'generators': [51, 576, 8, 32, 96], 'label': '1152.156064.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bt1.a1', 'projective_image': '576.8353', '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': '24.13'}
  • id: 60983063
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.d1.a1', '12.bp1.a1', '12.bs1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.l1.a1', '48.ct1.a1', '48.db1.a1', '72.bn1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1570, -1, 8302, -1, 1569, -1, 2022, -1], 'generators': [51, 384, 8, 96, 576], 'label': '1152.156064.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bu1.a1', 'projective_image': '576.8353', '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': '36.12'}
  • id: 60983064
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bq1.a1', '12.bv1.a1', '12.bz1.a1'], 'contains': ['48.a1.a1', '48.q1.a1', '48.r1.a1', '72.bp1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4271, -1, 4666, -1, 3486, -1, 5657, -1], 'generators': [1, 672, 576, 384, 8], 'label': '1152.156064.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bv1.a1', 'projective_image': '576.8353', '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': '16.14'}
  • id: 60983065
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.bw1', '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': ['8.g1.a1', '12.bq1.a1', '12.bw1.a1', '12.bz1.a1'], 'contains': ['48.a1.a1', '48.s1.a1', '48.t1.a1', '72.bq1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4199, -1, 4215, -1, 3237, -1, 5549, -1], 'generators': [17, 384, 96, 8, 576], 'label': '1152.156064.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bw1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983066
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.bn1.a1', '12.br1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.bo1.a1', '96.u1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3035, -1, 6616, -1, 934, -1, 2152, -1], 'generators': [60, 576, 32, 8, 96], 'label': '1152.156064.24.bx1.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.bx1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60983067
    {'ambient': '1152.156064', '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.b1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.g1.a1', '12.bz1.a1', '12.cc1.a1', '16.m1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3480, -1, 5555, -1, 1247, -1, 2874, -1], 'generators': [1, 672, 384, 60, 576, 8, 32], 'label': '1152.156064.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '576.8353', '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: 60983068
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.e1.a1', '12.bo1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.bp1.a1', '96.v1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3526, -1, 5308, -1, 1074, -1, 2548, -1], 'generators': [1, 576, 8, 32, 672], 'label': '1152.156064.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.by1.a1', 'projective_image': '576.8353', '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: 60983069
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.bz1', '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.g1.a1', '12.bo1.a1', '12.ca1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.bq1.a1', '96.w1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3242, -1, 5025, -1, 1125, -1, 2578, -1], 'generators': [17, 576, 8, 32, 672], 'label': '1152.156064.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '24.bz1.a1', 'projective_image': '576.8353', '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: 60983070
    {'ambient': '1152.156064', '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': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bt1.a1', '12.cd1.a1', '12.ce1.a1'], 'contains': ['48.u1.a1', '72.a1.a1', '96.x1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4744, -1, 5560, -1, 4885, -1, 3366, -1], 'generators': [4, 576, 416, 8, 96], 'label': '1152.156064.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.ca1.a1', 'projective_image': '576.8353', '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': '48.48'}
  • id: 60983071
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.cd1.a1'], 'contains': ['48.u1.a1', '72.bq1.a1', '96.y1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3568, -1, 4705, -1, 1854, -1, 3159, -1], 'generators': [17, 576, 8, 416, 672], 'label': '1152.156064.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cd1.a1', 'old_label': '24.cb1.a1', 'projective_image': '576.8353', '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: 60983072
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.h1.a1', '12.cf1.a1'], 'contains': ['48.v1.a1', '48.w1.a1', '48.be1.a1', '48.bh1.a1', '48.bu1.a1', '72.bs1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3729, -1, 7007, -1, 1448, -1, 2366, -1], 'generators': [3, 8, 4, 48, 32], 'label': '1152.156064.24.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': '576.8353', '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': '8.3'}
  • id: 60983073
    {'ambient': '1152.156064', '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': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '8.i1.a1', '12.cf1.a1'], 'contains': ['48.w1.a1', '48.x1.a1', '48.ci1.a1', '48.cj1.a1', '48.cm1.a1', '72.bv1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3817, -1, 5148, -1, 1803, -1, 2865, -1], 'generators': [1, 32, 4, 48, 8], 'label': '1152.156064.24.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': '576.8353', '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': '24.8'}
  • id: 60983074
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '8.j1.a1', '12.cf1.a1'], 'contains': ['48.w1.a1', '48.ck1.a1', '48.cl1.a1', '72.bw1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7429, -1, 3984, -1, 2548, -1, 4397, -1], 'generators': [2, 32, 48, 4, 8], 'label': '1152.156064.24.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': '576.8353', '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': '12.4'}
  • id: 60983075
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cf1', '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.g1.a1', '12.h1.a1'], 'contains': ['48.y1.a1', '48.z1.a1', '48.ba1.a1', '48.bd1.a1', '48.bg1.a1', '48.bp1.a1', '48.bv1.a1', '72.br1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2857, -1, 6856, -1, 4456, -1, 3644, -1], 'generators': [3, 384, 100, 48, 8], 'label': '1152.156064.24.cf1.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.cf1.a1', 'projective_image': '576.8353', '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: 60983076
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cg1', '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.h1.a1', '12.i1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.z1.a1', '48.bq1.a1', '48.bs1.a1', '48.bw1.a1', '72.bt1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6545, -1, 4876, -1, 7084, -1, 5030, -1], 'generators': [99, 384, 4, 48, 8], 'label': '1152.156064.24.cg1.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.cg1.a1', 'projective_image': '576.8353', '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: 60983077
    {'ambient': '1152.156064', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.ci1.a1'], 'contains': ['48.z1.a1', '48.ba1.a1', '48.br1.a1', '48.bt1.a1', '48.bx1.a1', '72.bu1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5751, -1, 4325, -1, 5649, -1, 5166, -1], 'generators': [675, 384, 100, 48, 8], 'label': '1152.156064.24.ch1.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.ch1.a1', 'projective_image': '576.8353', '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: 60983078
    {'ambient': '1152.156064', '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.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5268, -1, 4569, -1, 2532, -1, 3471, -1], 'generators': [1, 32, 8, 2, 384, 48, 4], 'label': '1152.156064.4.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': '576.8353', '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': '144.153'}
  • id: 60983112
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '8.m1.a1', '12.cf1.a1'], 'contains': ['48.bu1.a1', '48.ci1.a1', '48.cl1.a1', '72.cq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5027, -1, 4987, -1, 2135, -1, 3243, -1], 'generators': [1, 32, 18, 12, 8], 'label': '1152.156064.24.dg1.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.dg1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983079
    {'ambient': '1152.156064', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.i1.a1', '12.ci1.a2'], 'contains': ['48.z1.a1', '48.ba1.a1', '48.br1.a2', '48.bt1.a2', '48.bx1.a2', '72.bu1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5751, -1, 4522, -1, 5649, -1, 5075, -1], 'generators': [579, 384, 100, 48, 8], 'label': '1152.156064.24.ch1.a2', '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.ch1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983080
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.ci1', '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.k1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.bb1.a1', '48.by1.a1', '48.bz1.a1', '48.cg1.a1', '72.bv1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6648, -1, 2220, -1, 9013, -1, 7652, -1], 'generators': [1, 384, 4, 48, 8], 'label': '1152.156064.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.ci1.a1', 'projective_image': '576.8353', '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: 60983081
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.l1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.ca1.a1', '48.cb1.a1', '72.bw1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9339, -1, 1481, -1, 9696, -1, 7141, -1], 'generators': [2, 384, 48, 4, 8], 'label': '1152.156064.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cj1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983082
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.ck1', '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.k1.a1', '12.ci1.a1', '12.ci1.a2'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.cc1.a1', '48.cd1.a1', '48.ch1.a1', '72.bx1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6005, -1, 2027, -1, 8819, -1, 9111, -1], 'generators': [1, 384, 676, 48, 8], 'label': '1152.156064.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.ck1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983083
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.ci1.a1', '12.ci1.a2'], 'contains': ['48.ba1.a1', '48.ce1.a1', '48.cf1.a1', '72.by1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8514, -1, 449, -1, 8570, -1, 9641, -1], 'generators': [98, 384, 48, 676, 8], 'label': '1152.156064.24.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cl1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983084
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cm1', '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.h1.a1', '12.o1.a1'], 'contains': ['48.bc1.a1', '48.bd1.a1', '48.bf1.a1', '48.bj1.a1', '48.bm1.a1', '48.bq1.a1', '48.bv1.a1', '72.bz1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2683, -1, 6949, -1, 5135, -1, 3836, -1], 'generators': [3, 384, 100, 144, 8], 'label': '1152.156064.24.cm1.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.cm1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983085
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.p1.a1'], 'contains': ['48.bc1.a1', '48.bd1.a1', '48.bg1.a1', '48.bk1.a1', '48.bn1.a1', '48.br1.a1', '48.bx1.a2', '72.ca1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3080, -1, 6198, -1, 3849, -1, 3689, -1], 'generators': [3, 384, 100, 624, 8], 'label': '1152.156064.24.cn1.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.cn1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983086
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.p1.a1'], 'contains': ['48.bc1.a1', '48.bd1.a1', '48.bg1.a1', '48.bk1.a2', '48.bn1.a1', '48.br1.a2', '48.bx1.a1', '72.ca1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3080, -1, 5804, -1, 3849, -1, 3734, -1], 'generators': [99, 384, 100, 624, 8], 'label': '1152.156064.24.cn1.a2', '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.cn1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60983087
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.co1', '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.h1.a1', '12.p1.a1', '12.cj1.a1'], 'contains': ['48.d1.a1', '48.bc1.a1', '48.bg1.a1', '48.bl1.a1', '48.bw1.a1', '72.cb1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4505, -1, 5607, -1, 6977, -1, 4553, -1], 'generators': [3, 384, 4, 144, 8], 'label': '1152.156064.24.co1.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.co1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983088
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.r1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.d1.a1', '48.by1.a1', '48.ca1.a1', '72.cc1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8976, -1, 1431, -1, 9170, -1, 7317, -1], 'generators': [1, 8, 2, 384, 4], 'label': '1152.156064.24.cp1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cp1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983089
    {'ambient': '1152.156064', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.d1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.o1.a1', '12.p1.a1', '12.u1.a1', '12.bp1.a1', '12.bs1.a1', '18.i1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4363, 703, 5821, 7877, 4784, 9334, 4263, 9378], 'generators': [3, 8, 576, 4, 384, 48, 96], 'label': '1152.156064.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.d1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.153'}
  • id: 60983090
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cq1', '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.t1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.d1.a1', '48.bz1.a1', '48.cb1.a1', '72.cd1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9041, -1, 1798, -1, 9248, -1, 7089, -1], 'generators': [17, 384, 18, 4, 8], 'label': '1152.156064.24.cq1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cq1.a1', 'projective_image': '576.8353', '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: 60983091
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.k1.a1', '12.cf1.a1'], 'contains': ['48.bh1.a1', '48.ci1.a1', '48.ck1.a1', '72.cc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5886, -1, 4940, -1, 2281, -1, 3301, -1], 'generators': [1, 32, 2, 4, 8], 'label': '1152.156064.24.cr1.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.cr1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983092
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '8.l1.a1', '12.cf1.a1'], 'contains': ['48.bh1.a1', '48.cj1.a1', '48.cl1.a1', '72.cd1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5155, -1, 4751, -1, 2466, -1, 2935, -1], 'generators': [17, 32, 18, 4, 8], 'label': '1152.156064.24.cs1.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.cs1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983093
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '8.l1.a1'], 'contains': ['48.bi1.a1', '48.cn1.a1', '48.co1.a1', '72.cd1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6596, -1, 4154, -1, 5301, -1, 3978, -1], 'generators': [17, 416, 18, 4, 8], 'label': '1152.156064.24.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ct1.a1', 'old_label': '24.ct1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983094
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.u1.a1'], 'contains': ['48.bj1.a1', '48.bk1.a1', '48.bn1.a1', '48.bp1.a1', '48.br1.a2', '48.bt1.a1', '48.bv1.a1', '72.ce1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2901, -1, 5841, -1, 3902, -1, 3881, -1], 'generators': [675, 384, 100, 624, 8], 'label': '1152.156064.24.cu1.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.cu1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983113
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '8.n1.a1', '12.cf1.a1'], 'contains': ['48.bu1.a1', '48.cj1.a1', '48.ck1.a1', '72.cr1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5084, -1, 4379, -1, 2350, -1, 2994, -1], 'generators': [17, 32, 2, 12, 8], 'label': '1152.156064.24.dh1.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.dh1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60983095
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.u1.a1'], 'contains': ['48.bj1.a1', '48.bk1.a2', '48.bn1.a1', '48.bp1.a1', '48.br1.a1', '48.bt1.a2', '48.bv1.a1', '72.ce1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2901, -1, 6332, -1, 3902, -1, 3926, -1], 'generators': [579, 384, 100, 624, 8], 'label': '1152.156064.24.cu1.a2', '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.cu1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60983096
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cv1', '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.h1.a1', '12.u1.a1', '12.ck1.a1'], 'contains': ['48.e1.a1', '48.bj1.a1', '48.bl1.a1', '48.bp1.a1', '48.bs1.a1', '72.cf1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5218, -1, 5522, -1, 7030, -1, 4598, -1], 'generators': [99, 384, 4, 144, 8], 'label': '1152.156064.24.cv1.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.cv1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983097
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cw1', '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.i1.a1', '12.p1.a1', '12.u1.a1'], 'contains': ['48.bk1.a1', '48.bk1.a2', '48.bl1.a1', '48.br1.a1', '48.br1.a2', '48.bs1.a1', '48.bw1.a1', '72.cg1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6235, -1, 5655, -1, 6525, -1, 4181, -1], 'generators': [579, 384, 4, 144, 8], 'label': '1152.156064.24.cw1.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.cw1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983098
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cx1', '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.i1.a1', '12.o1.a1', '12.cl1.a1'], 'contains': ['48.bk1.a2', '48.bm1.a1', '48.bq1.a1', '48.bt1.a1', '48.bx1.a2', '72.ch1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5670, -1, 4288, -1, 5792, -1, 5121, -1], 'generators': [675, 384, 100, 144, 8], 'label': '1152.156064.24.cx1.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.cx1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983099
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cx1', '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.i1.a1', '12.o1.a1', '12.cl1.a2'], 'contains': ['48.bk1.a1', '48.bm1.a1', '48.bq1.a1', '48.bt1.a2', '48.bx1.a1', '72.ch1.a2'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5670, -1, 4622, -1, 5792, -1, 5211, -1], 'generators': [579, 384, 100, 144, 8], 'label': '1152.156064.24.cx1.a2', '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.cx1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983100
    {'ambient': '1152.156064', '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': '96.a1.a1', 'complements': ['192.b1.a1', '192.k1.a1', '192.b1.b1', '192.k1.b1', '192.n1.a1', '192.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.f1.a1', '18.l1.a1', '24.cr1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5929, 3117, 4650, 9177, 2263, 6915, 3388, 7115], 'generators': [1, 672, 32, 2, 576, 4, 8], 'label': '1152.156064.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.c1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '576.8353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 60983101
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.cy1', '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.k1.a1', '12.cj1.a1', '12.ck1.a1'], 'contains': ['48.bl1.a1', '48.bo1.a1', '48.by1.a1', '48.bz1.a1', '48.ch1.a1', '72.ci1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6704, -1, 2112, -1, 9309, -1, 7920, -1], 'generators': [1, 384, 4, 720, 8], 'label': '1152.156064.24.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cy1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983102
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.cj1.a1', '12.ck1.a1'], 'contains': ['48.bl1.a1', '48.ca1.a1', '48.cb1.a1', '72.cj1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9436, -1, 1696, -1, 9977, -1, 7435, -1], 'generators': [2, 384, 720, 4, 8], 'label': '1152.156064.24.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cz1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983103
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.da1', '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.k1.a1', '12.cl1.a1', '12.cl1.a2'], 'contains': ['48.bm1.a1', '48.bo1.a1', '48.cc1.a1', '48.cd1.a1', '48.cg1.a1', '72.ck1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5961, -1, 2064, -1, 8960, -1, 9156, -1], 'generators': [1, 384, 676, 720, 8], 'label': '1152.156064.24.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.da1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983104
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '72.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.cl1.a1', '12.cl1.a2'], 'contains': ['48.bm1.a1', '48.ce1.a1', '48.cf1.a1', '72.cl1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8471, -1, 562, -1, 8660, -1, 9686, -1], 'generators': [98, 384, 720, 676, 8], 'label': '1152.156064.24.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.db1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983105
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.ch1.a1', '12.ck1.a1'], 'contains': ['48.bs1.a1', '48.by1.a1', '48.ca1.a1', '72.cm1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7705, -1, 1529, -1, 9838, -1, 7860, -1], 'generators': [1, 8, 674, 384, 4], 'label': '1152.156064.24.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.dc1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983106
    {'ambient': '1152.156064', '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': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.ch1.a1', '12.ck1.a1'], 'contains': ['48.bs1.a1', '48.bz1.a1', '48.cb1.a1', '72.cn1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7770, -1, 1739, -1, 9916, -1, 7383, -1], 'generators': [17, 384, 594, 4, 8], 'label': '1152.156064.24.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.dd1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983107
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '12.ci1.a1', '12.cl1.a1'], 'contains': ['48.bt1.a1', '48.cc1.a1', '48.ce1.a1', '72.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7315, -1, 887, -1, 8889, -1, 9508, -1], 'generators': [1, 8, 578, 384, 676], 'label': '1152.156064.24.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.de1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983108
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '12.ci1.a2', '12.cl1.a2'], 'contains': ['48.bt1.a2', '48.cc1.a1', '48.ce1.a1', '72.co1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7315, -1, 828, -1, 8889, -1, 9582, -1], 'generators': [1, 8, 98, 384, 676], 'label': '1152.156064.24.de1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.de1.a2', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983109
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.df1', '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.bd1.a1', '12.ci1.a1', '12.cl1.a1'], 'contains': ['48.bt1.a1', '48.cd1.a1', '48.cf1.a1', '72.cp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7522, -1, 1071, -1, 8722, -1, 9261, -1], 'generators': [17, 384, 114, 580, 8], 'label': '1152.156064.24.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.df1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983110
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.df1', '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.bd1.a1', '12.ci1.a2', '12.cl1.a2'], 'contains': ['48.bt1.a2', '48.cd1.a1', '48.cf1.a1', '72.cp1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7522, -1, 942, -1, 8722, -1, 9381, -1], 'generators': [17, 384, 690, 580, 8], 'label': '1152.156064.24.df1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.df1.a2', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983111
    {'ambient': '1152.156064', '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.h1.a1', '12.j1.a1', '12.m1.a1', '12.q1.a1', '12.s1.a1', '12.be1.a1', '12.bg1.a1', '18.a1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8010, -1, 2952, -1, 6720, -1, 6177, -1], 'generators': [577, 8, 672, 578, 384, 48, 4], 'label': '1152.156064.6.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': '576.8353', '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: 60983114
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.di1', '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.bf1.a1', '12.cg1.a1', '12.ck1.a1'], 'contains': ['48.e1.a1', '48.by1.a1', '48.cb1.a1', '72.cq1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8408, -1, 2251, -1, 9528, -1, 7210, -1], 'generators': [65, 384, 18, 4, 8], 'label': '1152.156064.24.di1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.di1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983115
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.dj1', '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.n1.a1', '12.bh1.a1', '12.cg1.a1', '12.ck1.a1'], 'contains': ['48.e1.a1', '48.bz1.a1', '48.ca1.a1', '72.cr1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9301, -1, 1379, -1, 9565, -1, 7179, -1], 'generators': [49, 384, 2, 4, 8], 'label': '1152.156064.24.dj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.dj1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983116
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.dk1', '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.bf1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.bw1.a1', '48.by1.a1', '48.cb1.a1', '72.cs1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7653, -1, 2188, -1, 9741, -1, 7614, -1], 'generators': [65, 384, 594, 4, 8], 'label': '1152.156064.24.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.dk1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983117
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.dl1', '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.bh1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.bw1.a1', '48.bz1.a1', '48.ca1.a1', '72.ct1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8278, -1, 1354, -1, 9777, -1, 7527, -1], 'generators': [49, 384, 674, 4, 8], 'label': '1152.156064.24.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.dl1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983118
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dm1', '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.bj1.a1', '12.ci1.a1', '12.cl1.a2'], 'contains': ['48.bx1.a1', '48.cc1.a1', '48.cf1.a1', '72.cu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6836, -1, 1035, -1, 8615, -1, 9425, -1], 'generators': [65, 384, 114, 580, 8], 'label': '1152.156064.24.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.dm1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983119
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dm1', '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.bj1.a1', '12.ci1.a2', '12.cl1.a1'], 'contains': ['48.bx1.a2', '48.cc1.a1', '48.cf1.a1', '72.cu1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6836, -1, 1139, -1, 8615, -1, 9305, -1], 'generators': [65, 384, 690, 580, 8], 'label': '1152.156064.24.dm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.dm1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983120
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dn1', '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.bl1.a1', '12.ci1.a1', '12.cl1.a2'], 'contains': ['48.bx1.a1', '48.cd1.a1', '48.ce1.a1', '72.cv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6806, -1, 760, -1, 8774, -1, 9456, -1], 'generators': [49, 384, 578, 676, 8], 'label': '1152.156064.24.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.dn1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983121
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '24.dn1', '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.bl1.a1', '12.ci1.a2', '12.cl1.a1'], 'contains': ['48.bx1.a2', '48.cd1.a1', '48.ce1.a1', '72.cv1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6806, -1, 784, -1, 8774, -1, 9336, -1], 'generators': [49, 384, 98, 676, 8], 'label': '1152.156064.24.dn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.dn1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983122
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '6.d1', '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.h1.a1', '12.k1.a1', '12.l1.a1', '12.r1.a1', '12.t1.a1', '12.bf1.a1', '12.bh1.a1', '12.cg1.a1', '12.ch1.a1', '12.cj1.a1', '12.ck1.a1', '18.b1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8642, -1, 2085, -1, 8196, -1, 7594, -1], 'generators': [1, 8, 4, 2, 384, 48, 672], 'label': '1152.156064.6.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': '576.8353', '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: 60983123
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1'], 'contains': ['48.cp1.a1', '48.cq1.a1', '48.cr1.a1', '48.cs1.a1', '48.ct1.a1', '48.cu1.b1', '48.cv1.b1', '48.dc1.a1', '48.dd1.a1', '48.df1.a1', '48.df1.a2', '48.dg1.a1', '48.dg1.a2', '72.cw1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1238, -1, 8032, -1, 1299, -1, 1512, -1], 'generators': [3, 384, 584, 48, 96], 'label': '1152.156064.24.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.do1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983124
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1'], 'contains': ['48.cp1.b1', '48.cq1.b1', '48.cr1.b1', '48.cs1.a1', '48.ct1.a1', '48.cu1.a1', '48.cv1.a1', '48.dc1.b1', '48.dd1.b1', '48.df1.a1', '48.df1.a2', '48.dg1.a1', '48.dg1.a2', '72.cw1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1238, -1, 8557, -1, 1299, -1, 1460, -1], 'generators': [3, 384, 584, 624, 96], 'label': '1152.156064.24.do1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '24.do1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983125
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.bm1.a1'], 'contains': ['48.cw1.a1', '48.cy1.a1', '48.da1.a1', '72.cx1.a1', '96.bh1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [313, -1, 9832, -1, 175, -1, 242, -1], 'generators': [3, 576, 48, 32, 96], 'label': '1152.156064.24.dp1.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.dp1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 60983126
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.bm1.a1'], 'contains': ['48.cw1.b1', '48.cy1.a1', '48.da1.a1', '72.cx1.b1', '96.bh1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [313, -1, 9722, -1, 175, -1, 306, -1], 'generators': [3, 576, 56, 32, 96], 'label': '1152.156064.24.dp1.b1', '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.dp1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 60983127
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.bp1.a1'], 'contains': ['48.f1.a1', '48.cq1.a1', '48.cr1.a1', '48.cu1.a1', '48.cv1.a1', '48.cx1.a1', '48.db1.a1', '72.cx1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [542, -1, 9115, -1, 862, -1, 940, -1], 'generators': [3, 384, 48, 96, 576], 'label': '1152.156064.24.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.dq1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 60983128
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.bp1.a1'], 'contains': ['48.f1.b1', '48.cq1.b1', '48.cr1.b1', '48.cu1.b1', '48.cv1.b1', '48.cx1.a1', '48.db1.a1', '72.cx1.b1'], 'core': '48.f1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [542, -1, 9349, -1, 862, -1, 1034, -1], 'generators': [3, 384, 56, 96, 576], 'label': '1152.156064.24.dq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.dq1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 60983129
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '32.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': ['36.br1.a1', '36.bt1.a2', '36.bt1.a1', '36.bs1.a1', '36.bu1.a1', '36.bw1.a2', '36.bw1.a1', '36.bv1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.n1.a1', '16.o1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.bg1.a1', '128.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [47, 9297, 9949, 1234, 213, 1459, 193, 1251], 'generators': [32, 384, 672, 576], 'label': '1152.156064.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normal_contains': ['96.d1.a1', '96.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60983130
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '48.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.b1.b1', '96.a1.a1', '96.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1591, -1, 8158, -1, 865, -1, 785, -1], 'generators': [8, 48, 32, 384], 'label': '1152.156064.32.b1.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.b1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983131
    {'ambient': '1152.156064', 'aut_centralizer_order': 72, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.c1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '64.c1.a1', '96.h1.a1', '96.i1.a1', '96.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1626, -1, 7937, -1, 822, -1, 2072, -1], 'generators': [3, 8, 32, 384], 'label': '1152.156064.32.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': '576.8353', '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': '4.2'}
  • id: 60983132
    {'ambient': '1152.156064', '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': '96.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '16.c1.a1', '16.f1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '96.m1.a1', '96.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1662, -1, 7886, -1, 780, -1, 2023, -1], 'generators': [51, 8, 32, 384], 'label': '1152.156064.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.d1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983133
    {'ambient': '1152.156064', '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.i1.a1', '12.j1.a1', '12.l1.a1', '12.ba1.a1', '12.bc1.a1', '12.bi1.a1', '12.bk1.a1', '18.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7594, -1, 2891, -1, 6963, -1, 6232, -1], 'generators': [577, 8, 672, 2, 384, 48, 676], 'label': '1152.156064.6.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': '576.8353', '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: 60983134
    {'ambient': '1152.156064', 'aut_centralizer_order': 144, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '32.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.d1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '96.t1.a1', '96.x1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4534, -1, 5712, -1, 2473, -1, 3447, -1], 'generators': [4, 32, 384, 8], 'label': '1152.156064.32.e1.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.e1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983135
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '96.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '16.d1.a1', '16.f1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '96.u1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3193, -1, 6745, -1, 994, -1, 2446, -1], 'generators': [60, 32, 8, 384], 'label': '1152.156064.32.f1.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.f1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983136
    {'ambient': '1152.156064', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '16.e1.a1', '16.i1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.r1.a1', '96.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3547, -1, 5418, -1, 1277, -1, 2995, -1], 'generators': [1, 384, 8, 32], 'label': '1152.156064.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.g1.a1', 'projective_image': '576.8353', '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: 60983137
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '16.e1.a1', '16.j1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.s1.a1', '96.w1.a1', '96.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3401, -1, 4860, -1, 1708, -1, 3072, -1], 'generators': [17, 8, 32, 384], 'label': '1152.156064.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.h1.a1', 'projective_image': '576.8353', '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: 60983138
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '16.c1.a1'], 'contains': ['64.b1.a1', '64.c1.a1', '64.d1.a1', '96.bh1.a1', '96.bj1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [178, -1, 9757, -1, 266, -1, 296, -1], 'generators': [3, 48, 32, 384], 'label': '1152.156064.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '32.i1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983139
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '16.c1.a1'], 'contains': ['64.b1.b1', '64.c1.a1', '64.d1.a1', '96.bh1.b1', '96.bj1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [178, -1, 9550, -1, 266, -1, 399, -1], 'generators': [3, 56, 32, 384], 'label': '1152.156064.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '32.i1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983140
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.bt1.a1', '18.i1.a1', '18.l1.a1', '18.m1.a1'], 'contains': ['72.a1.a1', '72.k1.a1', '72.l1.a1', '72.t1.a1', '72.bm1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4063, 2709, 5727, 8597, 5005, 7487, 4700, 6940], 'generators': [3, 4, 96, 576], 'label': '1152.156064.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1'], 'normal_contains': ['72.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 60983141
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.e1.a1', '72.j1.a1', '72.k1.a1', '72.r1.a1', '72.u1.a1', '72.br1.a1', '72.bu1.a1', '72.bu1.a2', '72.ca1.a1', '72.ca1.a2', '72.ce1.a1', '72.ce1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3525, -1, 5832, -1, 3418, -1, 4034, -1], 'generators': [3, 580, 48, 96], 'label': '1152.156064.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.b1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983142
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.a1.a1', '18.b1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.i1.a1', '72.l1.a1', '72.v1.a1', '72.br1.a1', '72.bs1.a1', '72.bt1.a1', '72.bz1.a1', '72.cb1.a1', '72.cf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4239, -1, 6262, -1, 5912, -1, 4647, -1], 'generators': [3, 4, 48, 96], 'label': '1152.156064.36.c1.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.c1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983143
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.c1.a1', '18.d1.a1', '18.i1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.s1.a1', '72.t1.a1', '72.w1.a1', '72.bt1.a1', '72.bu1.a1', '72.bu1.a2', '72.cg1.a1', '72.ch1.a1', '72.ch1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6594, -1, 4756, -1, 5850, -1, 5455, -1], 'generators': [579, 4, 48, 96], 'label': '1152.156064.36.d1.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.d1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983144
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '6.f1', '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.k1.a1', '12.m1.a1', '12.bb1.a1', '12.bd1.a1', '12.bj1.a1', '12.bl1.a1', '12.ci1.a1', '12.ci1.a2', '12.cl1.a1', '12.cl1.a2', '18.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6885, -1, 1016, -1, 7640, -1, 8678, -1], 'generators': [1, 8, 676, 578, 384, 48, 672], 'label': '1152.156064.6.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': '576.8353', '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: 60983145
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.a1.a1', '18.c1.a1', '18.j1.a1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.x1.a1', '72.z1.a1', '72.bh1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7506, -1, 3324, -1, 5383, -1, 6585, -1], 'generators': [577, 4, 48], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983146
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.b1.a1', '18.d1.a1', '18.j1.a1'], 'contains': ['72.d1.a1', '72.g1.a1', '72.y1.a1', '72.ba1.a1', '72.bi1.a1', '72.bv1.a1', '72.bx1.a1', '72.ci1.a1', '72.ck1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8187, -1, 834, -1, 7681, -1, 8767, -1], 'generators': [1, 4, 48, 672], 'label': '1152.156064.36.f1.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.f1.a1', 'projective_image': '576.8353', '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: 60983147
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.b1.a1', '18.c1.a1', '18.k1.a1'], 'contains': ['72.d1.a1', '72.bb1.a1', '72.be1.a1', '72.bw1.a1', '72.cj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9991, -1, 1419, -1, 8210, -1, 8090, -1], 'generators': [2, 48, 672], 'label': '1152.156064.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983148
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.a1.a1', '18.d1.a1', '18.k1.a1'], 'contains': ['72.d1.a1', '72.bc1.a1', '72.bd1.a1', '72.by1.a1', '72.cl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9133, -1, 395, -1, 7315, -1, 9205, -1], 'generators': [578, 48, 672], 'label': '1152.156064.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983149
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.j1.a1'], 'contains': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '72.bf1.a1', '72.bg1.a1', '72.bj1.a1', '72.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6464, -1, 3463, -1, 4618, -1, 6359, -1], 'generators': [1, 580, 48], 'label': '1152.156064.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.i1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983150
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.i1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.k1.a1', '72.m1.a1', '72.o1.a1', '72.s1.a1', '72.u1.a1', '72.bz1.a1', '72.ca1.a1', '72.ca1.a2', '72.ce1.a1', '72.ce1.a2', '72.ch1.a1', '72.ch1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3625, -1, 5876, -1, 3554, -1, 4086, -1], 'generators': [3, 580, 624, 96], 'label': '1152.156064.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.j1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983151
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '72.bl1.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.j1.a1', '72.l1.a1', '72.n1.a1', '72.w1.a1', '72.ca1.a1', '72.ca1.a2', '72.cb1.a1', '72.cg1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4416, -1, 5621, -1, 5447, -1, 4330, -1], 'generators': [3, 4, 624, 96], 'label': '1152.156064.36.k1.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.k1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983152
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.a1.a1', '18.e1.a1', '18.l1.a1'], 'contains': ['72.l1.a1', '72.x1.a1', '72.bc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7948, -1, 2842, -1, 6427, -1, 6853, -1], 'generators': [577, 578], 'label': '1152.156064.36.l1.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.l1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983153
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.b1.a1', '18.f1.a1', '18.l1.a1'], 'contains': ['72.l1.a1', '72.y1.a1', '72.bb1.a1', '72.cc1.a1', '72.cm1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9730, -1, 1368, -1, 7875, -1, 8373, -1], 'generators': [1, 2, 672], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983154
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '18.a1.a1', '18.f1.a1', '18.m1.a1'], 'contains': ['72.l1.a1', '72.z1.a1', '72.bd1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7771, -1, 2690, -1, 6050, -1, 6953, -1], 'generators': [113, 114], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983155
    {'ambient': '1152.156064', '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.p1.a1', '12.q1.a1', '12.t1.a1', '12.v1.a1', '12.y1.a1', '12.bi1.a1', '12.bl1.a1', '18.e1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8119, -1, 2689, -1, 7210, -1, 6411, -1], 'generators': [577, 8, 672, 578, 384, 624, 4], 'label': '1152.156064.6.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': '576.8353', '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: 60983156
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '18.b1.a1', '18.e1.a1', '18.m1.a1'], 'contains': ['72.l1.a1', '72.ba1.a1', '72.be1.a1', '72.cd1.a1', '72.cn1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9071, -1, 1286, -1, 8136, -1, 7749, -1], 'generators': [17, 18, 576], 'label': '1152.156064.36.o1.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.o1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983157
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1'], 'contains': ['72.m1.a1', '72.n1.a1', '72.r1.a1', '72.t1.a1', '72.v1.a1', '72.ce1.a1', '72.ce1.a2', '72.cf1.a1', '72.cg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5028, -1, 5568, -1, 5509, -1, 4752, -1], 'generators': [579, 4, 624, 96], 'label': '1152.156064.36.p1.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.p1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983158
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.e1.a1', '18.g1.a1', '18.j1.a1'], 'contains': ['72.n1.a1', '72.p1.a1', '72.x1.a1', '72.ba1.a1', '72.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7348, -1, 3140, -1, 5743, -1, 6789, -1], 'generators': [577, 4, 624], 'label': '1152.156064.36.q1.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.q1.a1', 'projective_image': '576.8353', '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: 60983159
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.f1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.n1.a1', '72.q1.a1', '72.y1.a1', '72.z1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7299, -1, 3362, -1, 5698, -1, 6918, -1], 'generators': [1, 4, 624], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983160
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.f1.a1', '18.g1.a1', '18.k1.a1'], 'contains': ['72.n1.a1', '72.bb1.a1', '72.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9921, -1, 1498, -1, 6574, -1, 7999, -1], 'generators': [2, 624], 'label': '1152.156064.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983161
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.e1.a1', '18.h1.a1', '18.k1.a1'], 'contains': ['72.n1.a1', '72.bc1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9835, -1, 1528, -1, 6756, -1, 7961, -1], 'generators': [578, 624], 'label': '1152.156064.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983162
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.j1.a1'], 'contains': ['72.o1.a1', '72.p1.a1', '72.q1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1', '72.bi1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6419, -1, 3213, -1, 4673, -1, 6312, -1], 'generators': [1, 580, 624], 'label': '1152.156064.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.u1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983163
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.c1.a1', '18.g1.a1', '18.l1.a1'], 'contains': ['72.t1.a1', '72.x1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8004, -1, 2782, -1, 6715, -1, 6884, -1], 'generators': [577, 2], 'label': '1152.156064.36.v1.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.v1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983164
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.d1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.t1.a1', '72.y1.a1', '72.bc1.a1', '72.co1.a1', '72.co1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8886, -1, 457, -1, 7477, -1, 9052, -1], 'generators': [1, 578, 672], 'label': '1152.156064.36.w1.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.w1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983165
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.c1.a1', '18.h1.a1', '18.m1.a1'], 'contains': ['72.t1.a1', '72.z1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7741, -1, 2628, -1, 6390, -1, 7045, -1], 'generators': [113, 18], 'label': '1152.156064.36.x1.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.x1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983166
    {'ambient': '1152.156064', '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', '576.h1.a1', '576.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.k1.a1', '6.l1.a1', '6.n1.a1', '8.i1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4232, 7430, 5058, 2376, 1955, 2062, 3029, 2420], 'generators': [1, 32, 384, 4, 8, 576, 672, 48], 'label': '1152.156064.2.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.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '576.8353', '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': '576.8353'}
  • id: 60983167
    {'ambient': '1152.156064', '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.r1.a1', '12.s1.a1', '12.w1.a1', '12.x1.a1', '12.bj1.a1', '12.bk1.a1', '18.f1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7731, -1, 2512, -1, 6896, -1, 6680, -1], 'generators': [1, 8, 672, 2, 384, 624, 4], 'label': '1152.156064.6.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': '576.8353', '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: 60983168
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.d1.a1', '18.g1.a1', '18.m1.a1'], 'contains': ['72.t1.a1', '72.ba1.a1', '72.bd1.a1', '72.cp1.a1', '72.cp1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8715, -1, 549, -1, 7241, -1, 8831, -1], 'generators': [17, 114, 576], 'label': '1152.156064.36.y1.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.y1.a1', 'projective_image': '576.8353', '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: 60983169
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.a1.a1', '18.g1.a1', '18.n1.a1'], 'contains': ['72.v1.a1', '72.x1.a1', '72.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8059, -1, 2807, -1, 6169, -1, 6823, -1], 'generators': [161, 114], 'label': '1152.156064.36.z1.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.z1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983170
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.b1.a1', '18.h1.a1', '18.n1.a1'], 'contains': ['72.v1.a1', '72.y1.a1', '72.be1.a1', '72.cq1.a1', '72.cs1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9645, -1, 1575, -1, 7962, -1, 8300, -1], 'generators': [65, 18, 576], 'label': '1152.156064.36.ba1.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.ba1.a1', 'projective_image': '576.8353', '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: 60983171
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.a1.a1', '18.h1.a1', '18.o1.a1'], 'contains': ['72.v1.a1', '72.z1.a1', '72.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7801, -1, 2654, -1, 6134, -1, 7014, -1], 'generators': [625, 578], 'label': '1152.156064.36.bb1.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.bb1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983172
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.b1.a1', '18.g1.a1', '18.o1.a1'], 'contains': ['72.v1.a1', '72.ba1.a1', '72.bb1.a1', '72.cr1.a1', '72.ct1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9195, -1, 1019, -1, 8049, -1, 8226, -1], 'generators': [49, 2, 672], 'label': '1152.156064.36.bc1.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.bc1.a1', 'projective_image': '576.8353', '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: 60983173
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.c1.a1', '18.e1.a1', '18.n1.a1'], 'contains': ['72.w1.a1', '72.x1.a1', '72.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7918, -1, 2757, -1, 6679, -1, 6754, -1], 'generators': [161, 18], 'label': '1152.156064.36.bd1.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.bd1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983174
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.d1.a1', '18.f1.a1', '18.n1.a1'], 'contains': ['72.w1.a1', '72.y1.a1', '72.bd1.a1', '72.cu1.a1', '72.cu1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8788, -1, 886, -1, 7154, -1, 8904, -1], 'generators': [65, 114, 576], 'label': '1152.156064.36.be1.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.be1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983175
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.c1.a1', '18.f1.a1', '18.o1.a1'], 'contains': ['72.w1.a1', '72.z1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7711, -1, 2562, -1, 6354, -1, 6983, -1], 'generators': [625, 2], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983176
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '18.d1.a1', '18.e1.a1', '18.o1.a1'], 'contains': ['72.w1.a1', '72.ba1.a1', '72.bc1.a1', '72.cv1.a1', '72.cv1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8506, -1, 301, -1, 7390, -1, 8978, -1], 'generators': [49, 578, 672], 'label': '1152.156064.36.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': '576.8353', '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': '16.11'}
  • id: 60983177
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '12.bp1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.h1.a1', '72.m1.a1', '72.bl1.a1', '72.bm1.a1', '72.bn1.a1', '72.cw1.a1', '72.cw1.b1', '72.cx1.a1', '72.cx1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1565, -1, 8261, -1, 1678, -1, 1878, -1], 'generators': [3, 8, 48, 576, 96], 'label': '1152.156064.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.bh1.a1', 'projective_image': '576.8353', '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': '6.2'}
  • id: 60983178
    {'ambient': '1152.156064', '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.u1.a1', '12.v1.a1', '12.x1.a1', '12.ba1.a1', '12.bd1.a1', '12.be1.a1', '12.bh1.a1', '18.g1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8413, -1, 2656, -1, 7089, -1, 6451, -1], 'generators': [577, 8, 672, 2, 384, 624, 676], 'label': '1152.156064.6.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': '576.8353', '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: 60983179
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bn1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1'], 'contains': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '72.n1.a1', '72.o1.a1', '72.bl1.a1', '72.bo1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6543, -1, 3508, -1, 4399, -1, 5507, -1], 'generators': [4, 48, 96, 576], 'label': '1152.156064.36.bi1.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.bi1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983180
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.bj1', '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.bo1.a1', '12.bq1.a1', '18.j1.a1'], 'contains': ['72.f1.a1', '72.g1.a1', '72.p1.a1', '72.q1.a1', '72.bl1.a1', '72.bp1.a1', '72.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4884, -1, 4397, -1, 3622, -1, 6006, -1], 'generators': [1, 48, 576], 'label': '1152.156064.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.bj1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983181
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.bs1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.j1.a1', '72.r1.a1', '72.s1.a1', '72.bm1.a1', '72.bn1.a1', '72.bo1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3198, -1, 6835, -1, 2937, -1, 3427, -1], 'generators': [3, 60, 96, 576], 'label': '1152.156064.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.bk1.a1', 'projective_image': '576.8353', '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': '12.5'}
  • id: 60983182
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.bu1.a1', '18.i1.a1', '18.n1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.u1.a1', '72.v1.a1', '72.w1.a1', '72.bn1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5241, -1, 4163, -1, 4943, -1, 4880, -1], 'generators': [51, 4, 96, 576], 'label': '1152.156064.36.bl1.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.bl1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983183
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.bv1.a1', '18.j1.a1', '18.l1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.x1.a1', '72.y1.a1', '72.bf1.a1', '72.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7885, -1, 2590, -1, 5244, -1, 6499, -1], 'generators': [1, 4, 576], 'label': '1152.156064.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bm1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983184
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '12.ca1.a1', '12.cd1.a1', '18.j1.a1', '18.m1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.z1.a1', '72.ba1.a1', '72.bg1.a1', '72.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7652, -1, 2535, -1, 5199, -1, 6405, -1], 'generators': [17, 4, 96], 'label': '1152.156064.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bn1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983185
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bx1.a1', '18.k1.a1', '18.l1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.bb1.a1', '72.bc1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9798, -1, 1467, -1, 6010, -1, 7805, -1], 'generators': [2, 576], 'label': '1152.156064.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bo1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983186
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.cb1.a1', '12.ce1.a1', '18.k1.a1', '18.m1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.bd1.a1', '72.be1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9884, -1, 1859, -1, 5965, -1, 7693, -1], 'generators': [18, 96], 'label': '1152.156064.36.bp1.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.bp1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983187
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '36.bq1', '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.bz1.a1', '12.cc1.a1', '18.j1.a1'], 'contains': ['72.bh1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bo1.a1', '72.bp1.a1', '72.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5858, -1, 3991, -1, 3799, -1, 6087, -1], 'generators': [1, 60, 576], 'label': '1152.156064.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.bq1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983188
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '12.cg1.a1', '18.b1.a1'], 'contains': ['72.bs1.a1', '72.bv1.a1', '72.bw1.a1', '72.cc1.a1', '72.cd1.a1', '72.cq1.a1', '72.cr1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9292, -1, 1090, -1, 9083, -1, 8152, -1], 'generators': [1, 2, 48], 'label': '1152.156064.36.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.br1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983189
    {'ambient': '1152.156064', '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.u1.a1', '12.w1.a1', '12.y1.a1', '12.bb1.a1', '12.bc1.a1', '12.bf1.a1', '12.bg1.a1', '18.h1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7953, -1, 2587, -1, 7031, -1, 6739, -1], 'generators': [1, 8, 672, 578, 384, 624, 676], 'label': '1152.156064.6.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': '576.8353', '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: 60983190
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '18.b1.a1'], 'contains': ['72.bt1.a1', '72.bv1.a1', '72.bw1.a1', '72.cm1.a1', '72.cn1.a1', '72.cs1.a1', '72.ct1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9462, -1, 782, -1, 9626, -1, 8594, -1], 'generators': [1, 674, 48], 'label': '1152.156064.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.bs1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983191
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '18.d1.a1'], 'contains': ['72.bu1.a1', '72.bx1.a1', '72.by1.a1', '72.co1.a1', '72.cp1.a1', '72.cu1.a1', '72.cv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8359, -1, 27, -1, 8414, -1, 9893, -1], 'generators': [1, 578, 48], 'label': '1152.156064.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.bt1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983192
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a2', '18.d1.a1'], 'contains': ['72.bu1.a2', '72.bx1.a1', '72.by1.a1', '72.co1.a2', '72.cp1.a2', '72.cu1.a2', '72.cv1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8359, -1, 170, -1, 8414, -1, 9819, -1], 'generators': [1, 98, 48], 'label': '1152.156064.36.bt1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.bt1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983193
    {'ambient': '1152.156064', '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': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.b1.a1'], 'contains': ['72.cb1.a1', '72.cc1.a1', '72.cd1.a1', '72.ci1.a1', '72.cj1.a1', '72.cs1.a1', '72.ct1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9535, -1, 661, -1, 9380, -1, 8521, -1], 'generators': [1, 2, 720], 'label': '1152.156064.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.bu1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983194
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ck1.a1', '18.b1.a1'], 'contains': ['72.cf1.a1', '72.ci1.a1', '72.cj1.a1', '72.cm1.a1', '72.cn1.a1', '72.cq1.a1', '72.cr1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9365, -1, 722, -1, 9467, -1, 8447, -1], 'generators': [1, 674, 720], 'label': '1152.156064.36.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.bv1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983195
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1.a1', '18.d1.a1'], 'contains': ['72.ch1.a1', '72.ck1.a1', '72.cl1.a1', '72.co1.a1', '72.cp1.a1', '72.cu1.a2', '72.cv1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8287, -1, 230, -1, 8501, -1, 9745, -1], 'generators': [1, 578, 720], 'label': '1152.156064.36.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.bw1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983196
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1.a2', '18.d1.a1'], 'contains': ['72.ch1.a2', '72.ck1.a1', '72.cl1.a1', '72.co1.a2', '72.cp1.a2', '72.cu1.a1', '72.cv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8287, -1, 88, -1, 8501, -1, 9966, -1], 'generators': [1, 98, 720], 'label': '1152.156064.36.bw1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.bw1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983197
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '48.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.bq1.a1', '24.bu1.a1', '24.bv1.a1', '24.bw1.a1'], 'contains': ['96.d1.a1', '96.f1.a1', '96.ba1.a1', '144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1355, 6555, 8526, 2769, 2204, 4184, 2224, 3234], 'generators': [8, 96, 576, 384], 'label': '1152.156064.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.d1.a1', '144.a1.a1', '192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983213
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.i1.a1', '24.o1.a1', '24.s1.a1', '24.y1.a1', '24.bj1.a1', '24.bk1.a1'], 'contains': ['96.f1.a1', '96.p1.a1', '144.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6000, -1, 3004, -1, 4388, -1, 5904, -1], 'generators': [580, 96, 384, 8], 'label': '1152.156064.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.n1.a1', 'projective_image': '576.8353', '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: 60983198
    {'ambient': '1152.156064', '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.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.d1.a1', '24.bp1.a1', '24.br1.a1', '24.bt1.a1', '24.bx1.a1', '24.by1.a1', '24.bz1.a1'], 'contains': ['96.e1.a1', '144.a1.a1', '192.c1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1041, 7515, 8577, 3887, 433, 3275, 1534, 4084], 'generators': [8, 32, 96, 576], 'label': '1152.156064.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.d1.a1'], 'normal_contains': ['96.e1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '576.8353', '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: 60983199
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.e1.a1', '24.h1.a1', '24.cg1.a1', '24.ci1.a1', '24.cj1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '144.s1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6135, 3274, 3724, 4939, 6985, 6548, 5854, 6009], 'generators': [4, 48, 8, 384], 'label': '1152.156064.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.a1.a1', '24.e1.a1'], 'normal_contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983200
    {'ambient': '1152.156064', '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': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bm1.a1', '12.bn1.a1', '12.br1.a1', '12.bu1.a1', '18.i1.a1', '24.cc1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4078, -1, 6181, -1, 1736, -1, 2625, -1], 'generators': [3, 96, 8, 4, 576, 48, 32], 'label': '1152.156064.6.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': '576.8353', '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': '96.195'}
  • id: 60983201
    {'ambient': '1152.156064', 'aut_centralizer_order': 288, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.e1.a1', '24.p1.a1', '24.co1.a1', '24.cp1.a1', '24.cq1.a1'], 'contains': ['96.b1.a1', '96.h1.a1', '144.b1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4659, 1275, 6016, 7479, 7254, 8638, 4791, 8016], 'generators': [3, 4, 384, 8], 'label': '1152.156064.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['12.b1.a1', '24.e1.a1'], 'normal_contains': ['96.b1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60983202
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.e1', '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.h1.a1', '24.e1.a1', '24.z1.a1', '24.cv1.a1', '24.di1.a1', '24.dj1.a1'], 'contains': ['96.b1.a1', '96.n1.a1', '144.bl1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5373, 2018, 5303, 6305, 7298, 7935, 4829, 7359], 'generators': [51, 4, 8, 384], 'label': '1152.156064.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['12.d1.a1', '24.e1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983203
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '36.a1.a1', 'complements': ['24.cr1.a1', '24.dh1.a1', '24.dg1.a1', '24.cs1.a1', '24.ct1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.dq1.a1'], 'contains': ['96.d1.a1', '96.z1.a1', '96.bc1.a1', '144.cf1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [366, 8476, 9403, 417, 690, 2367, 527, 2100], 'generators': [48, 96, 576, 384], 'label': '1152.156064.48.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.d1.a1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60983204
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '36.a1.a1', 'complements': ['24.cr1.a1', '24.dh1.a1', '24.dg1.a1', '24.cs1.a1', '24.ct1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.a1', '24.dq1.b1'], 'contains': ['96.d1.a1', '96.z1.b1', '96.bc1.b1', '144.cf1.b1'], 'core': '48.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [366, 8476, 9581, 1820, 690, 2367, 684, 401], 'generators': [56, 96, 576, 384], 'label': '1152.156064.48.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.a1'], 'normal_contains': ['96.d1.a1', '192.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.f1.b1', 'projective_image': '1152.156064', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60983205
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '96.k1.a1', '96.z1.a1', '96.z1.b1', '96.bi1.a1', '96.bi1.b1', '144.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2634, -1, 6590, -1, 3296, -1, 3552, -1], 'generators': [8, 48, 96, 384], 'label': '1152.156064.48.g1.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.g1.a1', 'projective_image': '576.8353', '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': '6.1'}
  • id: 60983206
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.bq1.a1'], 'contains': ['96.f1.a1', '96.h1.a1', '96.l1.a1', '96.bb1.a1', '96.bl1.a1', '144.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2101, -1, 7535, -1, 2800, -1, 2552, -1], 'generators': [3, 8, 96, 384], 'label': '1152.156064.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983207
    {'ambient': '1152.156064', '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': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.l1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1'], 'contains': ['96.f1.a1', '96.k1.a1', '96.bc1.a1', '96.bc1.b1', '96.bm1.a1', '144.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2685, -1, 7193, -1, 3234, -1, 2814, -1], 'generators': [8, 624, 96, 384], 'label': '1152.156064.48.i1.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.i1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983208
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.o1.a1', '24.q1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '24.bq1.a1'], 'contains': ['96.f1.a1', '96.l1.a1', '96.bd1.a1', '96.bn1.a1', '144.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2242, -1, 6676, -1, 2739, -1, 3341, -1], 'generators': [579, 8, 96, 384], 'label': '1152.156064.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983209
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.k1', '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.f1.a1', '24.m1.a1', '24.q1.a1', '24.v1.a1', '24.y1.a1', '24.z1.a1', '24.bu1.a1'], 'contains': ['96.f1.a1', '96.n1.a1', '96.o1.a1', '96.be1.a1', '96.bo1.a1', '144.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2293, -1, 7361, -1, 2926, -1, 3237, -1], 'generators': [51, 8, 96, 384], 'label': '1152.156064.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983210
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.l1.a1', '24.n1.a1', '24.w1.a1', '24.y1.a1', '24.ba1.a1', '24.bu1.a1'], 'contains': ['96.f1.a1', '96.o1.a1', '96.bf1.a1', '96.bp1.a1', '144.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2408, -1, 6179, -1, 2645, -1, 3289, -1], 'generators': [627, 8, 96, 384], 'label': '1152.156064.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983211
    {'ambient': '1152.156064', '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': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.bn1.a1', '12.bo1.a1', '12.ca1.a1', '12.cc1.a1', '18.j1.a1', '24.cd1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4199, -1, 5058, -1, 1907, -1, 2976, -1], 'generators': [1, 672, 32, 4, 576, 48, 8], 'label': '1152.156064.6.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': '576.8353', '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': '96.195'}
  • id: 60983212
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.h1.a1', '24.p1.a1', '24.r1.a1', '24.x1.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', '24.bi1.a1'], 'contains': ['96.b1.a1', '96.f1.a1', '96.p1.a1', '144.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6995, -1, 2845, -1, 6926, -1, 6481, -1], 'generators': [4, 96, 384, 8], 'label': '1152.156064.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.m1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983214
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.h1.a1', '24.m1.a1', '24.s1.a1', '24.w1.a1', '24.bl1.a1', '24.bm1.a1'], 'contains': ['96.c1.a1', '96.f1.a1', '96.q1.a1', '144.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4447, -1, 4034, -1, 3931, -1, 4973, -1], 'generators': [60, 96, 8, 384], 'label': '1152.156064.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.o1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983215
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.i1.a1', '24.n1.a1', '24.r1.a1', '24.v1.a1', '24.bn1.a1', '24.bo1.a1'], 'contains': ['96.f1.a1', '96.q1.a1', '144.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4243, -1, 4103, -1, 3757, -1, 4917, -1], 'generators': [636, 96, 8, 384], 'label': '1152.156064.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.p1.a1', 'projective_image': '576.8353', '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: 60983216
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.t1.a1', '24.bb1.a1', '24.bj1.a1', '24.bl1.a1', '24.bn1.a1', '24.bv1.a1'], 'contains': ['96.f1.a1', '96.bq1.a1', '144.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3495, -1, 4672, -1, 4668, -1, 6266, -1], 'generators': [577, 672, 384, 680], 'label': '1152.156064.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.q1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983217
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.u1.a1', '24.bc1.a1', '24.bj1.a1', '24.bm1.a1', '24.bo1.a1', '24.bv1.a1'], 'contains': ['96.f1.a1', '96.r1.a1', '144.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5427, -1, 2574, -1, 5100, -1, 6842, -1], 'generators': [1, 672, 384, 8], 'label': '1152.156064.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.r1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983218
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.u1.a1', '24.bd1.a1', '24.bk1.a1', '24.bl1.a1', '24.bo1.a1', '24.bw1.a1'], 'contains': ['96.f1.a1', '96.br1.a1', '144.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3052, -1, 4617, -1, 4506, -1, 6321, -1], 'generators': [113, 576, 584, 384], 'label': '1152.156064.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.s1.a1', 'projective_image': '576.8353', '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: 60983219
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.t1.a1', '24.be1.a1', '24.bk1.a1', '24.bm1.a1', '24.bn1.a1', '24.bw1.a1'], 'contains': ['96.f1.a1', '96.s1.a1', '144.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5331, -1, 2530, -1, 5165, -1, 6725, -1], 'generators': [17, 576, 8, 384], 'label': '1152.156064.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.t1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983220
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.bs1.a1', '24.ca1.a1', '24.cb1.a1'], 'contains': ['96.bg1.a1', '144.a1.a1', '192.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [875, -1, 8366, -1, 2018, -1, 2121, -1], 'generators': [8, 416, 96, 576], 'label': '1152.156064.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '48.u1.a1', 'projective_image': '576.8353', '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': '24.12'}
  • id: 60983221
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '16.c1.a1', '24.cc1.a1'], 'contains': ['96.g1.a1', '96.i1.a1', '96.m1.a1', '96.bh1.a1', '96.bh1.b1', '144.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1482, -1, 8305, -1, 490, -1, 736, -1], 'generators': [3, 8, 48, 32], 'label': '1152.156064.48.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': '576.8353', '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': '2.1'}
  • id: 60983222
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.bn1.a1', '12.cb1.a1', '18.k1.a1', '24.ce1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6986, -1, 4144, -1, 2614, -1, 4329, -1], 'generators': [2, 672, 32, 48, 576, 4, 8], 'label': '1152.156064.6.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': '576.8353', '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': '48.48'}
  • id: 60983223
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '16.d1.a1', '24.cc1.a1', '24.cd1.a1', '24.ce1.a1'], 'contains': ['96.g1.a1', '96.t1.a1', '96.u1.a1', '144.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4062, -1, 6105, -1, 2076, -1, 2605, -1], 'generators': [4, 48, 32, 8], 'label': '1152.156064.48.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': '576.8353', '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': '4.2'}
  • id: 60983224
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '48.x1', '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.bo1.a1', '16.e1.a1', '24.cd1.a1'], 'contains': ['96.g1.a1', '96.v1.a1', '96.w1.a1', '144.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3958, -1, 4843, -1, 1074, -1, 2893, -1], 'generators': [1, 48, 8, 32], 'label': '1152.156064.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '48.x1.a1', 'projective_image': '576.8353', '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: 60983225
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.e1.a1', '24.f1.a1', '24.cf1.a1'], 'contains': ['96.a1.a1', '96.h1.a1', '96.n1.a1', '96.bj1.a1', '96.bj1.b1', '144.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2166, -1, 7589, -1, 3357, -1, 2500, -1], 'generators': [3, 8, 48, 384], 'label': '1152.156064.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.y1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983226
    {'ambient': '1152.156064', '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': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.g1.a1', '24.cf1.a1', '24.cg1.a1', '24.ch1.a1', '24.ch1.a2'], 'contains': ['96.a1.a1', '96.l1.a1', '96.o1.a1', '96.bk1.a1', '96.bk1.b1', '144.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2788, -1, 6374, -1, 4606, -1, 3500, -1], 'generators': [99, 8, 48, 384], 'label': '1152.156064.48.z1.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': '48.z1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983227
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.a1', '24.cf1.a1', '24.ch1.a1', '24.ch1.a2', '24.ck1.a1', '24.cl1.a1'], 'contains': ['96.a1.a1', '96.p1.a1', '96.q1.a1', '144.t1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5563, -1, 3045, -1, 5945, -1, 6088, -1], 'generators': [100, 48, 8, 384], 'label': '1152.156064.48.ba1.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.ba1.a1', 'projective_image': '576.8353', '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: 60983228
    {'ambient': '1152.156064', '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': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.k1.a1', '24.ci1.a1', '24.ck1.a1'], 'contains': ['96.a1.a1', '96.r1.a1', '96.s1.a1', '144.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5519, -1, 2410, -1, 6562, -1, 7113, -1], 'generators': [1, 48, 8, 384], 'label': '1152.156064.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.bb1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983229
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.l1.a1', '24.cm1.a1', '24.cn1.a1', '24.cn1.a2', '24.co1.a1'], 'contains': ['96.h1.a1', '96.k1.a1', '96.o1.a1', '96.bs1.a1', '96.bs1.b1', '144.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2357, -1, 7405, -1, 3418, -1, 2658, -1], 'generators': [3, 8, 144, 384], 'label': '1152.156064.48.bc1.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': '48.bc1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983230
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.p1.a1', '24.cf1.a1', '24.cm1.a1', '24.cn1.a1', '24.cn1.a2'], 'contains': ['96.h1.a1', '96.l1.a1', '96.p1.a1', '144.w1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2942, -1, 6415, -1, 5041, -1, 3994, -1], 'generators': [3, 100, 384, 8], 'label': '1152.156064.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bd1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60983231
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '16.f1.a1', '24.cc1.a1'], 'contains': ['96.i1.a1', '96.m1.a1', '96.u1.a1', '144.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2041, -1, 7977, -1, 934, -1, 2273, -1], 'generators': [3, 60, 32, 8], 'label': '1152.156064.48.be1.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.be1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983232
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.e1.a1', '24.m1.a1', '24.cm1.a1'], 'contains': ['96.c1.a1', '96.h1.a1', '96.n1.a1', '144.x1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2448, -1, 7159, -1, 4557, -1, 3665, -1], 'generators': [3, 60, 8, 384], 'label': '1152.156064.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.bf1.a1', 'projective_image': '576.8353', '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: 60983233
    {'ambient': '1152.156064', '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.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.j1.a1', '12.k1.a1', '12.n1.a1', '12.v1.a1', '12.w1.a1', '12.z1.a1', '12.bq1.a1', '12.bv1.a1', '12.bw1.a1', '12.bz1.a1', '18.j1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6456, -1, 3457, -1, 4866, -1, 5841, -1], 'generators': [1, 672, 8, 4, 384, 48, 576], 'label': '1152.156064.6.n1.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.n1.a1', 'projective_image': '576.8353', '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: 60983234
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bg1', '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.m1.a1', '24.n1.a1', '24.cf1.a1', '24.cn1.a1', '24.cn1.a2', '24.co1.a1'], 'contains': ['96.h1.a1', '96.o1.a1', '96.q1.a1', '144.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3853, -1, 5409, -1, 3808, -1, 3726, -1], 'generators': [3, 156, 8, 384], 'label': '1152.156064.48.bg1.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': '48.bg1.a1', 'projective_image': '576.8353', '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: 60983235
    {'ambient': '1152.156064', 'aut_centralizer_order': 72, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.g1.a1', '24.cc1.a1', '24.cr1.a1', '24.cs1.a1'], 'contains': ['96.i1.a1', '96.t1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4136, -1, 6452, -1, 2414, -1, 3127, -1], 'generators': [3, 4, 32, 8], 'label': '1152.156064.48.bh1.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.bh1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983236
    {'ambient': '1152.156064', 'aut_centralizer_order': 36, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '16.g1.a1', '24.ct1.a1'], 'contains': ['96.j1.a1', '96.x1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4181, -1, 6334, -1, 5298, -1, 3614, -1], 'generators': [3, 4, 416, 8], 'label': '1152.156064.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1.a1', 'old_label': '48.bi1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983237
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.q1.a1', '24.cm1.a1', '24.cu1.a1', '24.cu1.a2', '24.cv1.a1'], 'contains': ['96.k1.a1', '96.l1.a1', '96.n1.a1', '96.bt1.a1', '96.bt1.b1', '144.z1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2489, -1, 7264, -1, 3541, -1, 3394, -1], 'generators': [99, 8, 144, 384], 'label': '1152.156064.48.bj1.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': '48.bj1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983238
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.l1.a1', '24.q1.a1', '24.cn1.a1', '24.cu1.a1', '24.cw1.a1', '24.cx1.a2'], 'contains': ['96.k1.a1', '96.l1.a1', '96.o1.a1', '96.bu1.a1', '96.bu1.b1', '144.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2736, -1, 6718, -1, 3480, -1, 2710, -1], 'generators': [579, 8, 144, 384], 'label': '1152.156064.48.bk1.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': '48.bk1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983239
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.l1.a1', '24.q1.a1', '24.cn1.a2', '24.cu1.a2', '24.cw1.a1', '24.cx1.a1'], 'contains': ['96.k1.a1', '96.l1.a1', '96.o1.a1', '96.bu1.a2', '96.bu1.b2', '144.ba1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2736, -1, 6762, -1, 3480, -1, 2762, -1], 'generators': [675, 8, 144, 384], 'label': '1152.156064.48.bk1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bk1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983240
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.r1.a1', '24.co1.a1', '24.cv1.a1', '24.cw1.a1', '24.cy1.a1', '24.cz1.a1'], 'contains': ['96.b1.a1', '96.k1.a1', '96.q1.a1', '144.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6091, -1, 3504, -1, 7961, -1, 6044, -1], 'generators': [4, 144, 8, 384], 'label': '1152.156064.48.bl1.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.bl1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983241
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.s1.a1', '24.cm1.a1', '24.cx1.a1', '24.cx1.a2', '24.da1.a1', '24.db1.a1'], 'contains': ['96.c1.a1', '96.k1.a1', '96.p1.a1', '144.bc1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5608, -1, 3248, -1, 5998, -1, 6133, -1], 'generators': [100, 144, 8, 384], 'label': '1152.156064.48.bm1.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.bm1.a1', 'projective_image': '576.8353', '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: 60983242
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.r1.a1', '24.s1.a1', '24.cn1.a1', '24.cn1.a2', '24.cu1.a1', '24.cu1.a2'], 'contains': ['96.k1.a1', '96.p1.a1', '96.q1.a1', '144.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5269, -1, 3822, -1, 4267, -1, 4746, -1], 'generators': [100, 624, 8, 384], 'label': '1152.156064.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bn1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983243
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.cy1.a1', '24.da1.a1'], 'contains': ['96.k1.a1', '96.r1.a1', '96.s1.a1', '144.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5769, -1, 2155, -1, 7908, -1, 7372, -1], 'generators': [1, 720, 8, 384], 'label': '1152.156064.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.bo1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983244
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.l1.a1', '12.m1.a1', '12.x1.a1', '12.y1.a1', '12.bx1.a1', '12.by1.a1', '18.k1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8891, -1, 1860, -1, 7150, -1, 7769, -1], 'generators': [2, 8, 672, 48, 384, 576, 4], 'label': '1152.156064.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.o1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983245
    {'ambient': '1152.156064', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.v1.a1', '24.cf1.a1', '24.cu1.a1', '24.cu1.a2', '24.cv1.a1'], 'contains': ['96.l1.a1', '96.n1.a1', '96.q1.a1', '144.bf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2840, -1, 6535, -1, 3880, -1, 3848, -1], 'generators': [99, 156, 8, 384], 'label': '1152.156064.48.bp1.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': '48.bp1.a1', 'projective_image': '576.8353', '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: 60983246
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bq1', '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.m1.a1', '24.w1.a1', '24.cg1.a1', '24.cm1.a1', '24.cx1.a1', '24.cx1.a2'], 'contains': ['96.c1.a1', '96.l1.a1', '96.o1.a1', '144.bg1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3010, -1, 5339, -1, 5660, -1, 4381, -1], 'generators': [99, 60, 8, 384], 'label': '1152.156064.48.bq1.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': '48.bq1.a1', 'projective_image': '576.8353', '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: 60983247
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.v1.a1', '24.w1.a1', '24.ch1.a1', '24.cn1.a1', '24.cu1.a2', '24.cw1.a1'], 'contains': ['96.l1.a1', '96.o1.a1', '96.q1.a1', '144.bh1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2980, -1, 5953, -1, 3844, -1, 3955, -1], 'generators': [675, 156, 8, 384], 'label': '1152.156064.48.br1.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': '48.br1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983248
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.v1.a1', '24.w1.a1', '24.ch1.a2', '24.cn1.a2', '24.cu1.a1', '24.cw1.a1'], 'contains': ['96.l1.a1', '96.o1.a1', '96.q1.a1', '144.bh1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2980, -1, 5617, -1, 3844, -1, 3925, -1], 'generators': [579, 156, 8, 384], 'label': '1152.156064.48.br1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.br1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60983249
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.x1.a1', '24.cg1.a1', '24.cv1.a1', '24.cw1.a1', '24.dc1.a1', '24.dd1.a1'], 'contains': ['96.b1.a1', '96.l1.a1', '144.bi1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6884, -1, 4769, -1, 8050, -1, 5099, -1], 'generators': [99, 4, 384, 8], 'label': '1152.156064.48.bs1.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': '48.bs1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983250
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.x1.a1', '24.ch1.a1', '24.cu1.a1', '24.cx1.a1', '24.de1.a1', '24.df1.a1'], 'contains': ['96.l1.a1', '96.p1.a1', '144.bj1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5863, -1, 4305, -1, 6706, -1, 5432, -1], 'generators': [675, 100, 384, 8], 'label': '1152.156064.48.bt1.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': '48.bt1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983251
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.x1.a1', '24.ch1.a2', '24.cu1.a2', '24.cx1.a2', '24.de1.a2', '24.df1.a2'], 'contains': ['96.l1.a1', '96.p1.a1', '144.bj1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5863, -1, 4409, -1, 6706, -1, 5523, -1], 'generators': [579, 100, 384, 8], 'label': '1152.156064.48.bt1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bt1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a2', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60983252
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '16.h1.a1', '24.cc1.a1', '24.dg1.a1', '24.dh1.a1'], 'contains': ['96.m1.a1', '96.t1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4717, -1, 6063, -1, 2324, -1, 2944, -1], 'generators': [51, 4, 32, 8], 'label': '1152.156064.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.bu1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983253
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bv1', '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.y1.a1', '24.z1.a1', '24.cf1.a1', '24.cm1.a1', '24.cu1.a1', '24.cu1.a2'], 'contains': ['96.n1.a1', '96.o1.a1', '96.p1.a1', '144.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3329, -1, 5385, -1, 5573, -1, 4214, -1], 'generators': [51, 100, 8, 384], 'label': '1152.156064.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bv1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983254
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.bw1', '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.ba1.a1', '24.cg1.a1', '24.co1.a1', '24.cw1.a1', '24.dk1.a1', '24.dl1.a1'], 'contains': ['96.b1.a1', '96.o1.a1', '144.bm1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6844, -1, 4068, -1, 8005, -1, 5061, -1], 'generators': [147, 4, 8, 384], 'label': '1152.156064.48.bw1.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.bw1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983255
    {'ambient': '1152.156064', '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.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.q1.a1', '12.r1.a1', '12.ba1.a1', '12.bb1.a1', '12.bv1.a1', '12.bx1.a1', '18.l1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8348, -1, 2357, -1, 6807, -1, 6604, -1], 'generators': [1, 672, 4, 2, 8, 576, 384], 'label': '1152.156064.6.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': '576.8353', '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: 60983256
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bx1', '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.y1.a1', '24.ba1.a1', '24.ch1.a1', '24.cn1.a2', '24.cx1.a2', '24.dm1.a1', '24.dn1.a1'], 'contains': ['96.o1.a1', '96.p1.a1', '144.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6055, -1, 3755, -1, 5901, -1, 5303, -1], 'generators': [723, 100, 8, 384], 'label': '1152.156064.48.bx1.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.bx1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983257
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bx1', '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.y1.a1', '24.ba1.a1', '24.ch1.a2', '24.cn1.a1', '24.cx1.a1', '24.dm1.a2', '24.dn1.a2'], 'contains': ['96.o1.a1', '96.p1.a1', '144.bn1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6055, -1, 3693, -1, 5901, -1, 5274, -1], 'generators': [627, 100, 8, 384], 'label': '1152.156064.48.bx1.a2', '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.bx1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a2', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60983258
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.bc1.a1', '24.ci1.a1', '24.cp1.a1', '24.cy1.a1', '24.dc1.a1', '24.di1.a1', '24.dk1.a1'], 'contains': ['96.b1.a1', '96.r1.a1', '144.bo1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7069, -1, 2300, -1, 8420, -1, 7281, -1], 'generators': [1, 4, 384, 8], 'label': '1152.156064.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.by1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983259
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.be1.a1', '24.ci1.a1', '24.cq1.a1', '24.cy1.a1', '24.dd1.a1', '24.dj1.a1', '24.dl1.a1'], 'contains': ['96.b1.a1', '96.s1.a1', '144.bp1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7359, -1, 1985, -1, 8465, -1, 7210, -1], 'generators': [17, 4, 8, 384], 'label': '1152.156064.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bz1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983260
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.bf1.a1', '24.cj1.a1', '24.cp1.a1', '24.cz1.a1', '24.dc1.a1', '24.dj1.a1', '24.dl1.a1'], 'contains': ['96.b1.a1', '144.bq1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8774, -1, 1911, -1, 9331, -1, 7181, -1], 'generators': [2, 384, 4, 8], 'label': '1152.156064.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.ca1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983261
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bi1.a1', '24.cj1.a1', '24.cq1.a1', '24.cz1.a1', '24.dd1.a1', '24.di1.a1', '24.dk1.a1'], 'contains': ['96.b1.a1', '144.br1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8608, -1, 2081, -1, 9388, -1, 7075, -1], 'generators': [18, 4, 8, 384], 'label': '1152.156064.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.cb1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983262
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '24.ck1.a1', '24.da1.a1', '24.de1.a1', '24.de1.a2', '24.dm1.a1', '24.dm1.a2'], 'contains': ['96.p1.a1', '96.r1.a1', '144.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6179, -1, 1952, -1, 7855, -1, 9097, -1], 'generators': [1, 676, 384, 8], 'label': '1152.156064.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.cc1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983263
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '24.ck1.a1', '24.da1.a1', '24.df1.a1', '24.df1.a2', '24.dn1.a1', '24.dn1.a2'], 'contains': ['96.p1.a1', '96.s1.a1', '144.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6218, -1, 1887, -1, 7720, -1, 9059, -1], 'generators': [17, 580, 8, 384], 'label': '1152.156064.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.cd1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983264
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.cl1.a1', '24.db1.a1', '24.de1.a1', '24.de1.a2', '24.dn1.a1', '24.dn1.a2'], 'contains': ['96.p1.a1', '144.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7675, -1, 1053, -1, 7630, -1, 9165, -1], 'generators': [98, 384, 676, 8], 'label': '1152.156064.48.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.ce1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983265
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.cl1.a1', '24.db1.a1', '24.df1.a1', '24.df1.a2', '24.dm1.a1', '24.dm1.a2'], 'contains': ['96.p1.a1', '144.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7804, -1, 1191, -1, 7595, -1, 9135, -1], 'generators': [114, 580, 8, 384], 'label': '1152.156064.48.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.cf1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983266
    {'ambient': '1152.156064', '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.b1.a1', '12.s1.a1', '12.t1.a1', '12.bc1.a1', '12.bd1.a1', '12.bw1.a1', '12.by1.a1', '18.m1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7799, -1, 2286, -1, 6640, -1, 6351, -1], 'generators': [17, 8, 576, 18, 384, 96, 4], 'label': '1152.156064.6.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': '576.8353', '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: 60983267
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cg1', '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.m1.a1', '24.bm1.a1', '24.ci1.a1', '24.da1.a1'], 'contains': ['96.c1.a1', '96.r1.a1', '96.s1.a1', '144.bw1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5481, -1, 2463, -1, 6607, -1, 7151, -1], 'generators': [1, 60, 8, 384], 'label': '1152.156064.48.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.cg1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983268
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.ch1', '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.bm1.a1', '24.ck1.a1', '24.cy1.a1'], 'contains': ['96.q1.a1', '96.r1.a1', '96.s1.a1', '144.bx1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5706, -1, 2196, -1, 7756, -1, 7410, -1], 'generators': [1, 732, 8, 384], 'label': '1152.156064.48.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.ch1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983269
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '16.i1.a1', '24.cd1.a1', '24.cr1.a1', '24.dg1.a1'], 'contains': ['96.t1.a1', '96.v1.a1', '144.bo1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4809, -1, 5248, -1, 2369, -1, 3196, -1], 'generators': [1, 4, 8, 32], 'label': '1152.156064.48.ci1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.ci1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983270
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '16.j1.a1', '24.cd1.a1', '24.cs1.a1', '24.dh1.a1'], 'contains': ['96.t1.a1', '96.w1.a1', '144.bp1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4754, -1, 4738, -1, 2524, -1, 3165, -1], 'generators': [17, 4, 8, 32], 'label': '1152.156064.48.cj1.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.cj1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983271
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '16.k1.a1', '24.ce1.a1', '24.cr1.a1', '24.dh1.a1'], 'contains': ['96.t1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7267, -1, 3779, -1, 2560, -1, 4625, -1], 'generators': [2, 4, 8, 32], 'label': '1152.156064.48.ck1.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.ck1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983272
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '16.l1.a1', '24.ce1.a1', '24.cs1.a1', '24.dg1.a1'], 'contains': ['96.t1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7206, -1, 4159, -1, 2596, -1, 4595, -1], 'generators': [18, 4, 8, 32], 'label': '1152.156064.48.cl1.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.cl1.a1', 'projective_image': '576.8353', '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: 60983273
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '48.cm1', '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.cc1.a1', '16.m1.a1', '24.cd1.a1'], 'contains': ['96.u1.a1', '96.v1.a1', '96.w1.a1', '144.bw1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3736, -1, 4878, -1, 1328, -1, 3038, -1], 'generators': [1, 60, 8, 32], 'label': '1152.156064.48.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '48.cm1.a1', 'projective_image': '576.8353', '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: 60983274
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '16.j1.a1', '24.ct1.a1'], 'contains': ['96.x1.a1', '96.y1.a1', '144.bp1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4852, -1, 4346, -1, 5624, -1, 3695, -1], 'generators': [17, 4, 8, 416], 'label': '1152.156064.48.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ct1.a1', 'old_label': '48.cn1.a1', 'projective_image': '576.8353', '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': '24.8'}
  • id: 60983275
    {'ambient': '1152.156064', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '16.l1.a1', '24.ct1.a1'], 'contains': ['96.x1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7236, -1, 3668, -1, 5696, -1, 4656, -1], 'generators': [18, 4, 8, 416], 'label': '1152.156064.48.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ct1.a1', 'old_label': '48.co1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983276
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.do1.a1'], 'contains': ['96.z1.a1', '96.ba1.a1', '96.bc1.b1', '96.bi1.a1', '96.bm1.a1', '144.by1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1101, -1, 7682, -1, 1655, -1, 1304, -1], 'generators': [584, 48, 96, 384], 'label': '1152.156064.48.cp1.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.cp1.a1', 'projective_image': '1152.156064', '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': '12.4'}
  • id: 60983277
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '2.c1', '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.g1.a1', '576.h1.a1', '576.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.m1.a1', '6.o1.a1', '8.j1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6936, 8521, 4009, 3380, 2694, 1030, 4386, 1454], 'generators': [2, 32, 384, 48, 8, 576, 672, 4], 'label': '1152.156064.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '576.8353', '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': '288.1028'}
  • id: 60983278
    {'ambient': '1152.156064', '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': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.ca1.a1', '12.cb1.a1', '18.m1.a1', '24.cs1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5316, -1, 4497, -1, 2458, -1, 3056, -1], 'generators': [17, 672, 32, 18, 576, 4, 8], 'label': '1152.156064.6.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': '576.8353', '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': '96.195'}
  • id: 60983279
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.do1.b1'], 'contains': ['96.z1.b1', '96.ba1.a1', '96.bc1.a1', '96.bi1.b1', '96.bm1.a1', '144.by1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1101, -1, 8737, -1, 1655, -1, 1200, -1], 'generators': [584, 624, 96, 384], 'label': '1152.156064.48.cp1.b1', '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.cp1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983280
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.do1.a1', '24.dq1.a1'], 'contains': ['96.z1.a1', '96.bb1.a1', '96.be1.a1', '96.bj1.a1', '96.bk1.a1', '96.bs1.a1', '96.bt1.a1', '144.bz1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [719, -1, 8081, -1, 1438, -1, 1356, -1], 'generators': [3, 48, 96, 384], 'label': '1152.156064.48.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cq1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983281
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.do1.b1', '24.dq1.b1'], 'contains': ['96.z1.b1', '96.bb1.a1', '96.be1.a1', '96.bj1.b1', '96.bk1.b1', '96.bs1.b1', '96.bt1.b1', '144.bz1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [719, -1, 8981, -1, 1438, -1, 1408, -1], 'generators': [3, 56, 96, 384], 'label': '1152.156064.48.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cq1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983282
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.do1.a1', '24.dq1.a1'], 'contains': ['96.z1.a1', '96.bd1.a1', '96.bf1.a1', '96.bk1.a1', '96.bu1.a1', '96.bu1.a2', '144.ca1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [567, -1, 7895, -1, 1199, -1, 992, -1], 'generators': [579, 48, 96, 384], 'label': '1152.156064.48.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cr1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983283
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.do1.b1', '24.dq1.b1'], 'contains': ['96.z1.b1', '96.bd1.a1', '96.bf1.a1', '96.bk1.b1', '96.bu1.b1', '96.bu1.b2', '144.ca1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [567, -1, 9261, -1, 1199, -1, 1096, -1], 'generators': [579, 56, 96, 384], 'label': '1152.156064.48.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cr1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983284
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.ba1.a1', '96.bb1.a1', '96.bd1.a1', '96.bl1.a1', '96.bn1.a1', '144.cb1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1178, -1, 9024, -1, 1561, -1, 1252, -1], 'generators': [3, 584, 96, 384], 'label': '1152.156064.48.cs1.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': '48.cs1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983285
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.ba1.a1', '96.be1.a1', '96.bf1.a1', '96.bo1.a1', '96.bp1.a1', '144.cc1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1229, -1, 8938, -1, 1500, -1, 1460, -1], 'generators': [51, 584, 96, 384], 'label': '1152.156064.48.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.ct1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983286
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.do1.b1', '24.dq1.a1'], 'contains': ['96.bb1.a1', '96.bc1.a1', '96.bf1.a1', '96.bs1.a1', '96.bu1.a1', '96.bu1.a2', '144.cd1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [650, -1, 9120, -1, 1138, -1, 888, -1], 'generators': [3, 624, 96, 384], 'label': '1152.156064.48.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cu1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983287
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.do1.a1', '24.dq1.b1'], 'contains': ['96.bb1.a1', '96.bc1.b1', '96.bf1.a1', '96.bs1.b1', '96.bu1.b1', '96.bu1.b2', '144.cd1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [650, -1, 9319, -1, 1138, -1, 1044, -1], 'generators': [3, 632, 96, 384], 'label': '1152.156064.48.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cu1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983288
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.do1.b1', '24.dq1.a1'], 'contains': ['96.bc1.a1', '96.bd1.a1', '96.be1.a1', '96.bt1.a1', '96.bu1.a1', '96.bu1.a2', '144.ce1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [770, -1, 9077, -1, 1377, -1, 940, -1], 'generators': [579, 624, 96, 384], 'label': '1152.156064.48.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cv1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983289
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['12.bt1.a1', '12.cd1.a1', '12.ce1.a1', '18.m1.a1', '24.ct1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6507, -1, 4223, -1, 4927, -1, 3820, -1], 'generators': [17, 672, 416, 18, 576, 4, 8], 'label': '1152.156064.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '6.s1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60983290
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.do1.a1', '24.dq1.b1'], 'contains': ['96.bc1.b1', '96.bd1.a1', '96.be1.a1', '96.bt1.b1', '96.bu1.b1', '96.bu1.b2', '144.ce1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [770, -1, 9212, -1, 1377, -1, 1148, -1], 'generators': [579, 632, 96, 384], 'label': '1152.156064.48.cv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.cv1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983291
    {'ambient': '1152.156064', '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': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.bp1.a1', '24.dp1.a1'], 'contains': ['96.e1.a1', '144.cf1.a1', '192.f1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [92, -1, 9684, -1, 160, -1, 251, -1], 'generators': [48, 32, 96, 576], 'label': '1152.156064.48.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cw1.a1', 'projective_image': '1152.156064', '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: 60983292
    {'ambient': '1152.156064', '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': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.bp1.a1', '24.dp1.b1'], 'contains': ['96.e1.a1', '144.cf1.b1', '192.f1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [92, -1, 9721, -1, 160, -1, 354, -1], 'generators': [56, 32, 96, 576], 'label': '1152.156064.48.cw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cw1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60983293
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bq1.a1', '24.dq1.a1', '24.dq1.b1'], 'contains': ['96.d1.a1', '96.bb1.a1', '96.bd1.a1', '144.cg1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [418, -1, 9528, -1, 628, -1, 580, -1], 'generators': [3, 96, 576, 384], 'label': '1152.156064.48.cx1.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.cx1.a1', 'projective_image': '1152.156064', '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': '6.2'}
  • id: 60983294
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.br1.a1', '24.dp1.a1', '24.dp1.b1'], 'contains': ['96.e1.a1', '144.cg1.a1', '192.i1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [48, -1, 9973, -1, 91, -1, 90, -1], 'generators': [3, 32, 96, 576], 'label': '1152.156064.48.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.cy1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 60983295
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '96.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bs1.a1'], 'contains': ['96.bg1.a1', '144.cg1.a1', '192.j1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [223, -1, 9904, -1, 334, -1, 19, -1], 'generators': [3, 416, 96, 576], 'label': '1152.156064.48.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '48.cz1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 60983296
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.bt1.a1', '24.dp1.a1', '24.dp1.b1'], 'contains': ['96.e1.a1', '144.ch1.a1', '192.m1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [306, -1, 9857, -1, 23, -1, 135, -1], 'generators': [51, 32, 96, 576], 'label': '1152.156064.48.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '48.da1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.da1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 60983297
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.bu1.a1', '24.dq1.a1', '24.dq1.b1'], 'contains': ['96.d1.a1', '96.be1.a1', '96.bf1.a1', '144.ch1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [493, -1, 9623, -1, 567, -1, 632, -1], 'generators': [51, 96, 576, 384], 'label': '1152.156064.48.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.db1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.db1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 60983298
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.do1.a1'], 'contains': ['96.bi1.a1', '96.bj1.a1', '96.bk1.a1', '96.bl1.a1', '96.bo1.a1', '96.bs1.b1', '96.bt1.b1', '144.ci1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 8199, -1, 1761, -1, 1870, -1], 'generators': [3, 104, 48, 384], 'label': '1152.156064.48.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dc1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983299
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.do1.b1'], 'contains': ['96.bi1.b1', '96.bj1.b1', '96.bk1.b1', '96.bl1.a1', '96.bo1.a1', '96.bs1.a1', '96.bt1.a1', '144.ci1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 8028, -1, 1761, -1, 1818, -1], 'generators': [3, 104, 144, 384], 'label': '1152.156064.48.dc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dc1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983300
    {'ambient': '1152.156064', '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': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.bu1.a1', '12.cb1.a1', '18.n1.a1', '24.dg1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5104, -1, 4708, -1, 2117, -1, 3347, -1], 'generators': [1, 672, 32, 18, 576, 12, 8], 'label': '1152.156064.6.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': '576.8353', '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': '96.195'}
  • id: 60983301
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.do1.a1'], 'contains': ['96.bi1.a1', '96.bk1.a1', '96.bn1.a1', '96.bp1.a1', '96.bu1.b1', '96.bu1.b2', '144.cj1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1879, -1, 7006, -1, 1884, -1, 1974, -1], 'generators': [579, 104, 48, 384], 'label': '1152.156064.48.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dd1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983302
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.do1.b1'], 'contains': ['96.bi1.b1', '96.bk1.b1', '96.bn1.a1', '96.bp1.a1', '96.bu1.a1', '96.bu1.a2', '144.cj1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1879, -1, 6881, -1, 1884, -1, 1922, -1], 'generators': [579, 104, 144, 384], 'label': '1152.156064.48.dd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dd1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983303
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1'], 'contains': ['96.bi1.a1', '96.bq1.a1', '96.br1.a1', '144.ck1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3254, -1, 5113, -1, 4446, -1, 5705, -1], 'generators': [97, 48, 680, 384], 'label': '1152.156064.48.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.de1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983304
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1'], 'contains': ['96.bi1.b1', '96.bq1.a1', '96.br1.a1', '144.ck1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3254, -1, 5065, -1, 4446, -1, 5660, -1], 'generators': [97, 720, 680, 384], 'label': '1152.156064.48.de1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.de1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983305
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.bl1.a1', '96.bm1.a1', '96.bp1.a1', '96.bs1.a1', '96.bs1.b1', '96.bu1.a2', '96.bu1.b1', '144.cl1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1794, -1, 7811, -1, 1823, -1, 1610, -1], 'generators': [3, 104, 624, 384], 'label': '1152.156064.48.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.df1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983306
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.bl1.a1', '96.bm1.a1', '96.bp1.a1', '96.bs1.a1', '96.bs1.b1', '96.bu1.a1', '96.bu1.b2', '144.cl1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1794, -1, 7725, -1, 1823, -1, 1662, -1], 'generators': [3, 104, 720, 384], 'label': '1152.156064.48.df1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.df1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983307
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.bm1.a1', '96.bn1.a1', '96.bo1.a1', '96.bt1.a1', '96.bt1.b1', '96.bu1.a2', '96.bu1.b1', '144.cm1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1930, -1, 7853, -1, 1945, -1, 1714, -1], 'generators': [579, 104, 720, 384], 'label': '1152.156064.48.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dg1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983308
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.do1.a1', '24.do1.b1'], 'contains': ['96.bm1.a1', '96.bn1.a1', '96.bo1.a1', '96.bt1.a1', '96.bt1.b1', '96.bu1.a1', '96.bu1.b2', '144.cm1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1930, -1, 7768, -1, 1945, -1, 1766, -1], 'generators': [579, 104, 624, 384], 'label': '1152.156064.48.dg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '48.dg1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983309
    {'ambient': '1152.156064', '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.g1.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.c1.a1', '192.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1501, -1, 7310, -1, 1094, -1, 2248, -1], 'generators': [8, 32, 384], 'label': '1152.156064.64.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': '576.8353', '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: 60983310
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '48.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '32.b1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '192.b1.a1', '192.f1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [142, -1, 8853, -1, 672, -1, 518, -1], 'generators': [48, 32, 384], 'label': '1152.156064.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.b1.a1', 'projective_image': '1152.156064', '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: 60983311
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.bu1.a1', '12.ca1.a1', '18.o1.a1', '24.dh1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5157, -1, 4257, -1, 2410, -1, 3096, -1], 'generators': [17, 672, 32, 2, 576, 12, 8], 'label': '1152.156064.6.u1.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.u1.a1', 'projective_image': '576.8353', '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': '96.195'}
  • id: 60983312
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '48.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '32.b1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.b1.b1', '192.f1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [142, -1, 9535, -1, 672, -1, 576, -1], 'generators': [56, 32, 384], 'label': '1152.156064.64.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.b1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983313
    {'ambient': '1152.156064', 'aut_centralizer_order': 72, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '32.c1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.h1.a1', '192.i1.a1', '192.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [72, -1, 9973, -1, 619, -1, 382, -1], 'generators': [3, 32, 384], 'label': '1152.156064.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '64.c1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983314
    {'ambient': '1152.156064', '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': '96.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '32.d1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.m1.a1', '192.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [261, -1, 9810, -1, 565, -1, 473, -1], 'generators': [51, 32, 384], 'label': '1152.156064.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '64.d1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983315
    {'ambient': '1152.156064', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.d1.a1', '24.ca1.a1', '36.a1.a1', '36.bi1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.i1.a1', '144.j1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 5240, 2772, 6287, 5471, 5639, 5995, 5160], 'generators': [4, 96, 576], 'label': '1152.156064.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.b1.a1', '24.d1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983316
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.b1.a1', '36.c1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.g1.a1', '144.q1.a1', '144.r1.a1', '144.v1.a1', '144.z1.a1', '144.bz1.a1', '144.bz1.b1', '144.ci1.a1', '144.ci1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2330, -1, 7856, -1, 2973, -1, 2377, -1], 'generators': [3, 8, 48, 96], 'label': '1152.156064.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.b1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983317
    {'ambient': '1152.156064', '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': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.b1.a1', '36.d1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.h1.a1', '144.r1.a1', '144.ba1.a1', '144.ba1.a2', '144.ca1.a1', '144.ca1.b1', '144.cj1.a1', '144.cj1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3218, -1, 6762, -1, 2847, -1, 2404, -1], 'generators': [579, 8, 48, 96], 'label': '1152.156064.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.c1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983318
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.i1.a1', '144.k1.a1', '144.s1.a1', '144.t1.a1', '144.bb1.a1', '144.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6935, -1, 2877, -1, 6236, -1, 6534, -1], 'generators': [4, 48, 96], 'label': '1152.156064.72.d1.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.d1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983319
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.b1.a1', '36.i1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.j1.a1', '144.l1.a1', '144.t1.a1', '144.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6024, -1, 3793, -1, 4210, -1, 5753, -1], 'generators': [580, 48, 96], 'label': '1152.156064.72.e1.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.e1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983320
    {'ambient': '1152.156064', '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': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.e1.a1', '36.i1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.m1.a1', '144.o1.a1', '144.ck1.a1', '144.ck1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4970, -1, 4307, -1, 4731, -1, 6427, -1], 'generators': [577, 48, 672], 'label': '1152.156064.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.f1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983321
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.f1.a1', '36.i1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.n1.a1', '144.p1.a1', '144.u1.a1', '144.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6707, -1, 2320, -1, 5355, -1, 6926, -1], 'generators': [1, 48, 672], 'label': '1152.156064.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.g1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983322
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '6.v1', '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.be1.a1', '12.bf1.a1', '12.bi1.a1', '12.bj1.a1', '12.bv1.a1', '12.by1.a1', '18.n1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8074, -1, 2415, -1, 6460, -1, 6286, -1], 'generators': [65, 8, 576, 18, 384, 96, 4], 'label': '1152.156064.6.v1.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.v1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983323
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.j1.a1', '36.k1.a1', '36.bh1.a1'], 'contains': ['144.d1.a1', '144.e1.a1', '144.h1.a1', '144.v1.a1', '144.ba1.a1', '144.ba1.a2', '144.cd1.a1', '144.cd1.b1', '144.cl1.a1', '144.cl1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2290, -1, 7878, -1, 2692, -1, 2322, -1], 'generators': [3, 8, 624, 96], 'label': '1152.156064.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.h1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983324
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.i1', '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': ['24.m1.a1', '36.c1.a1', '36.j1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.g1.a1', '144.k1.a1', '144.x1.a1', '144.y1.a1', '144.bf1.a1', '144.bg1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3435, -1, 6472, -1, 3653, -1, 3764, -1], 'generators': [3, 60, 96], 'label': '1152.156064.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.i1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983325
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.b1.a1', '36.k1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.h1.a1', '144.l1.a1', '144.y1.a1', '144.bh1.a1', '144.bh1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3632, -1, 5677, -1, 3078, -1, 3810, -1], 'generators': [3, 636, 96], 'label': '1152.156064.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.j1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983326
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.a1.a1', '36.b1.a1', '36.j1.a1'], 'contains': ['144.d1.a1', '144.f1.a1', '144.j1.a1', '144.w1.a1', '144.bj1.a1', '144.bj1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3677, -1, 5587, -1, 4045, -1, 4556, -1], 'generators': [3, 580, 96], 'label': '1152.156064.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983327
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.a1.a1', '36.c1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.i1.a1', '144.w1.a1', '144.bi1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4535, -1, 5973, -1, 6294, -1, 5144, -1], 'generators': [3, 4, 96], 'label': '1152.156064.72.l1.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.l1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983328
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.j1.a1', '36.p1.a1', '36.bh1.a1'], 'contains': ['144.e1.a1', '144.f1.a1', '144.g1.a1', '144.z1.a1', '144.ba1.a1', '144.ba1.a2', '144.ce1.a1', '144.ce1.b1', '144.cm1.a1', '144.cm1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2780, -1, 7418, -1, 2880, -1, 2350, -1], 'generators': [579, 8, 624, 96], 'label': '1152.156064.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.m1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983329
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.k1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '36.bi1.a1'], 'contains': ['144.e1.a1', '144.i1.a1', '144.l1.a1', '144.bb1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6610, -1, 3525, -1, 5745, -1, 6375, -1], 'generators': [4, 624, 96], 'label': '1152.156064.72.n1.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.n1.a1', 'projective_image': '576.8353', '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: 60983330
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.j1.a1', '36.u1.a1', '36.bi1.a1'], 'contains': ['144.e1.a1', '144.j1.a1', '144.k1.a1', '144.bc1.a1', '144.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5973, -1, 3578, -1, 4325, -1, 5806, -1], 'generators': [580, 624, 96], 'label': '1152.156064.72.o1.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.o1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983331
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.q1.a1', '36.u1.a1', '36.bj1.a1'], 'contains': ['144.e1.a1', '144.m1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5128, -1, 4046, -1, 4902, -1, 6610, -1], 'generators': [577, 624], 'label': '1152.156064.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.p1.a1', 'projective_image': '576.8353', '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: 60983332
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.q1', '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.u1.a1', '36.r1.a1', '36.u1.a1', '36.bj1.a1'], 'contains': ['144.e1.a1', '144.n1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5027, -1, 4014, -1, 4821, -1, 6648, -1], 'generators': [1, 624], 'label': '1152.156064.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.q1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983333
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '6.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': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.bg1.a1', '12.bh1.a1', '12.bk1.a1', '12.bl1.a1', '12.bw1.a1', '12.bx1.a1', '18.o1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7881, -1, 2206, -1, 6541, -1, 6515, -1], 'generators': [49, 8, 672, 2, 384, 576, 4], 'label': '1152.156064.6.w1.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.w1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983334
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '36.b1.a1', '36.p1.a1', '36.bk1.a1'], 'contains': ['144.f1.a1', '144.g1.a1', '144.l1.a1', '144.bf1.a1', '144.bh1.a1', '144.bh1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3391, -1, 6211, -1, 3132, -1, 3886, -1], 'generators': [579, 636, 96], 'label': '1152.156064.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.r1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983335
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '36.d1.a1', '36.j1.a1', '36.bk1.a1'], 'contains': ['144.f1.a1', '144.h1.a1', '144.k1.a1', '144.bg1.a1', '144.bh1.a1', '144.bh1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3996, -1, 5841, -1, 3598, -1, 4176, -1], 'generators': [579, 60, 96], 'label': '1152.156064.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.s1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983336
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '36.a1.a1', '36.d1.a1', '36.p1.a1', '36.v1.a1', '36.w1.a1', '36.x1.a1', '36.y1.a1'], 'contains': ['144.f1.a1', '144.i1.a1', '144.bi1.a1', '144.bj1.a1', '144.bj1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6425, -1, 4533, -1, 6178, -1, 6216, -1], 'generators': [579, 4, 96], 'label': '1152.156064.72.t1.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.t1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983337
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.b1.a1', '36.j1.a1', '36.bl1.a1'], 'contains': ['144.g1.a1', '144.h1.a1', '144.j1.a1', '144.bk1.a1', '144.bn1.a1', '144.bn1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4210, -1, 4705, -1, 3991, -1, 4511, -1], 'generators': [51, 580, 96], 'label': '1152.156064.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.u1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983338
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '36.c1.a1', '36.p1.a1', '36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bc1.a1', '36.bl1.a1'], 'contains': ['144.g1.a1', '144.i1.a1', '144.bk1.a1', '144.bl1.a1', '144.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5336, -1, 4867, -1, 6402, -1, 5190, -1], 'generators': [51, 4, 96], 'label': '1152.156064.72.v1.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.v1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983339
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '36.d1.a1', '36.k1.a1', '36.bd1.a1', '36.be1.a1', '36.bf1.a1', '36.bg1.a1', '36.bl1.a1'], 'contains': ['144.h1.a1', '144.i1.a1', '144.bm1.a1', '144.bn1.a1', '144.bn1.a2'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6818, -1, 3681, -1, 6125, -1, 5615, -1], 'generators': [627, 4, 96], 'label': '1152.156064.72.w1.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.w1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983340
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '36.e1.a1', '36.l1.a1', '36.q1.a1', '36.v1.a1', '36.z1.a1', '36.bd1.a1', '36.bm1.a1'], 'contains': ['144.i1.a1', '144.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7398, -1, 3048, -1, 6079, -1, 7013, -1], 'generators': [577, 4], 'label': '1152.156064.72.x1.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': '72.x1.a1', 'projective_image': '576.8353', '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': '16.11'}
  • id: 60983341
    {'ambient': '1152.156064', '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.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '36.f1.a1', '36.m1.a1', '36.r1.a1', '36.w1.a1', '36.ba1.a1', '36.be1.a1', '36.bm1.a1'], 'contains': ['144.i1.a1', '144.n1.a1', '144.bo1.a1', '144.bs1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8300, -1, 1982, -1, 7038, -1, 7905, -1], 'generators': [1, 4, 672], 'label': '1152.156064.72.y1.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': '72.y1.a1', 'projective_image': '576.8353', '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: 60983342
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '36.e1.a1', '36.n1.a1', '36.r1.a1', '36.x1.a1', '36.bb1.a1', '36.bf1.a1', '36.bn1.a1'], 'contains': ['144.i1.a1', '144.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7368, -1, 2994, -1, 6043, -1, 7044, -1], 'generators': [113, 4], 'label': '1152.156064.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.z1.a1', 'projective_image': '576.8353', '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: 60983343
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.f1.a1', '36.o1.a1', '36.q1.a1', '36.y1.a1', '36.bc1.a1', '36.bg1.a1', '36.bn1.a1'], 'contains': ['144.i1.a1', '144.p1.a1', '144.bp1.a1', '144.bt1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7819, -1, 1306, -1, 7093, -1, 7748, -1], 'generators': [17, 4, 576], 'label': '1152.156064.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '576.8353', '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: 60983344
    {'ambient': '1152.156064', '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': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.a1.a1', '24.bp1.a1', '32.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1240, 8797, 8432, 1747, 804, 1310, 1659, 1216], 'generators': [8, 384, 576, 48, 32, 672], 'label': '1152.156064.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.b1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '576.8353', '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': '144.183'}
  • id: 60983345
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '36.g1.a1', '36.m1.a1', '36.s1.a1', '36.v1.a1', '36.bc1.a1', '36.bf1.a1', '36.bo1.a1'], 'contains': ['144.i1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9568, -1, 1723, -1, 7146, -1, 7448, -1], 'generators': [2, 672], 'label': '1152.156064.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bb1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983346
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '36.h1.a1', '36.l1.a1', '36.t1.a1', '36.w1.a1', '36.bb1.a1', '36.bg1.a1', '36.bo1.a1'], 'contains': ['144.i1.a1', '144.bu1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8512, -1, 744, -1, 6509, -1, 8544, -1], 'generators': [578, 672], 'label': '1152.156064.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bc1.a1', 'projective_image': '576.8353', '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: 60983347
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '36.h1.a1', '36.n1.a1', '36.s1.a1', '36.y1.a1', '36.z1.a1', '36.be1.a1', '36.bp1.a1'], 'contains': ['144.i1.a1', '144.bv1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8922, -1, 1499, -1, 6455, -1, 8329, -1], 'generators': [114, 576], 'label': '1152.156064.72.bd1.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.bd1.a1', 'projective_image': '576.8353', '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: 60983348
    {'ambient': '1152.156064', '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': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.g1.a1', '36.o1.a1', '36.t1.a1', '36.x1.a1', '36.ba1.a1', '36.bd1.a1', '36.bp1.a1'], 'contains': ['144.i1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9495, -1, 2077, -1, 7200, -1, 7327, -1], 'generators': [18, 576], 'label': '1152.156064.72.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': '576.8353', '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': '4.2'}
  • id: 60983349
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '36.i1.a1', '36.u1.a1', '36.bm1.a1'], 'contains': ['144.j1.a1', '144.m1.a1', '144.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6569, -1, 2726, -1, 5252, -1, 6885, -1], 'generators': [1, 580], 'label': '1152.156064.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.bf1.a1', 'projective_image': '576.8353', '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: 60983350
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bg1', '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.bk1.a1', '36.i1.a1', '36.u1.a1', '36.bn1.a1'], 'contains': ['144.j1.a1', '144.o1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6218, -1, 2701, -1, 5216, -1, 6799, -1], 'generators': [17, 100], 'label': '1152.156064.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bg1.a1', 'projective_image': '576.8353', '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: 60983351
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '36.e1.a1', '36.u1.a1', '36.bq1.a1'], 'contains': ['144.k1.a1', '144.m1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5269, -1, 3869, -1, 4780, -1, 6576, -1], 'generators': [577, 60], 'label': '1152.156064.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bh1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983352
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.f1.a1', '36.u1.a1', '36.bq1.a1'], 'contains': ['144.k1.a1', '144.n1.a1', '144.p1.a1', '144.bw1.a1', '144.bx1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6659, -1, 2370, -1, 5413, -1, 6975, -1], 'generators': [1, 60, 672], 'label': '1152.156064.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bi1.a1', 'projective_image': '576.8353', '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: 60983353
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bj1', '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.bn1.a1', '36.i1.a1', '36.q1.a1', '36.bq1.a1'], 'contains': ['144.l1.a1', '144.m1.a1', '144.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5832, -1, 3723, -1, 4942, -1, 6682, -1], 'generators': [577, 636], 'label': '1152.156064.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bj1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983354
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '36.i1.a1', '36.r1.a1', '36.bq1.a1'], 'contains': ['144.l1.a1', '144.n1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5765, -1, 3759, -1, 4861, -1, 6769, -1], 'generators': [1, 636], 'label': '1152.156064.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bk1.a1', 'projective_image': '576.8353', '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: 60983355
    {'ambient': '1152.156064', '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': '96.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.d1.a1', '24.ca1.a1', '32.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4781, 5517, 5763, 5114, 2099, 3499, 3144, 4619], 'generators': [4, 576, 672, 32, 384, 8], 'label': '1152.156064.8.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.b1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '576.8353', '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': '96.226'}
  • id: 60983356
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.bp1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.e1.a1', '144.by1.a1', '144.by1.b1', '144.cf1.a1', '144.cf1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1002, -1, 8570, -1, 2251, -1, 1571, -1], 'generators': [8, 48, 96, 576], 'label': '1152.156064.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bl1.a1', 'projective_image': '576.8353', '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': '6.1'}
  • id: 60983357
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '24.br1.a1', '24.bs1.a1', '36.a1.a1', '36.bh1.a1', '36.bk1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.f1.a1', '144.cb1.a1', '144.cg1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1329, -1, 8684, -1, 2157, -1, 2157, -1], 'generators': [3, 8, 96, 576], 'label': '1152.156064.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bm1.a1', 'projective_image': '576.8353', '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': '6.2'}
  • id: 60983358
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bu1.a1', '36.bh1.a1', '36.bk1.a1', '36.bl1.a1'], 'contains': ['144.a1.a1', '144.g1.a1', '144.h1.a1', '144.cc1.a1', '144.ch1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1419, -1, 8593, -1, 2124, -1, 2184, -1], 'generators': [51, 8, 96, 576], 'label': '1152.156064.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bn1.a1', 'projective_image': '576.8353', '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': '6.2'}
  • id: 60983359
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.bx1.a1', '36.bi1.a1', '36.bk1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.k1.a1', '144.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5579, -1, 3935, -1, 3020, -1, 4697, -1], 'generators': [60, 96, 576], 'label': '1152.156064.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bo1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983360
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '72.bp1', '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.bv1.a1', '24.by1.a1', '36.bj1.a1', '36.bm1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.m1.a1', '144.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5069, -1, 4344, -1, 3701, -1, 6175, -1], 'generators': [1, 576], 'label': '1152.156064.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.bp1.a1', 'projective_image': '576.8353', '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': '8.5'}
  • id: 60983361
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '24.bz1.a1', '24.cb1.a1', '36.bj1.a1', '36.bn1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.o1.a1', '144.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4788, -1, 4108, -1, 3181, -1, 5950, -1], 'generators': [17, 96], 'label': '1152.156064.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.bq1.a1', 'projective_image': '576.8353', '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: 60983362
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['144.q1.a1', '144.r1.a1', '144.t1.a1', '144.w1.a1', '144.y1.a1', '144.bf1.a1', '144.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3722, -1, 6172, -1, 4988, -1, 4039, -1], 'generators': [3, 100, 48], 'label': '1152.156064.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.br1.a1', 'projective_image': '576.8353', '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: 60983363
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.cc1.a1', '36.c1.a1', '36.br1.a1'], 'contains': ['144.b1.a1', '144.q1.a1', '144.s1.a1', '144.x1.a1', '144.bl1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4355, -1, 6135, -1, 6348, -1, 4419, -1], 'generators': [3, 4, 48], 'label': '1152.156064.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.a1', 'projective_image': '576.8353', '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: 60983364
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.c1.a1', '36.d1.a1', '36.bs1.a1'], 'contains': ['144.r1.a1', '144.s1.a1', '144.bg1.a1', '144.bi1.a1', '144.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6469, -1, 4667, -1, 6868, -1, 5236, -1], 'generators': [99, 4, 48], 'label': '1152.156064.72.bt1.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.bt1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983365
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '36.b1.a1', '36.d1.a1', '36.bt1.a1'], 'contains': ['144.r1.a1', '144.t1.a1', '144.bh1.a1', '144.bj1.a1', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5677, -1, 4426, -1, 5803, -1, 5478, -1], 'generators': [675, 100, 48], 'label': '1152.156064.72.bu1.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.bu1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983366
    {'ambient': '1152.156064', '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.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '24.bx1.a1', '32.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3193, 7561, 6627, 2884, 1020, 2479, 2160, 2315], 'generators': [60, 384, 576, 32, 8, 672], 'label': '1152.156064.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '576.8353', '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: 60983367
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a2', '36.b1.a1', '36.d1.a1', '36.bt1.a2'], 'contains': ['144.r1.a1', '144.t1.a1', '144.bh1.a2', '144.bj1.a2', '144.bn1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5677, -1, 4496, -1, 5803, -1, 5341, -1], 'generators': [579, 100, 48], 'label': '1152.156064.72.bu1.a2', '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.bu1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983368
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.a1', '24.ci1.a1', '36.f1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.s1.a1', '144.u1.a1', '144.bo1.a1', '144.bp1.a1', '144.bw1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7718, -1, 1049, -1, 8104, -1, 7826, -1], 'generators': [1, 4, 48], 'label': '1152.156064.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.bv1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983369
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1.a1', '24.cj1.a1', '36.g1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.s1.a1', '144.bq1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9641, -1, 1687, -1, 8366, -1, 7494, -1], 'generators': [2, 48], 'label': '1152.156064.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.bw1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983370
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.f1.a1', '36.bt1.a1', '36.bt1.a2'], 'contains': ['144.t1.a1', '144.u1.a1', '144.bs1.a1', '144.bt1.a1', '144.bx1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7505, -1, 351, -1, 7675, -1, 9203, -1], 'generators': [1, 676, 48], 'label': '1152.156064.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.bx1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983371
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.h1.a1', '36.bt1.a1', '36.bt1.a2'], 'contains': ['144.t1.a1', '144.bu1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8397, -1, 468, -1, 7342, -1, 9555, -1], 'generators': [98, 48], 'label': '1152.156064.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.by1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983372
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '36.c1.a1', '36.j1.a1'], 'contains': ['144.v1.a1', '144.w1.a1', '144.x1.a1', '144.z1.a1', '144.bc1.a1', '144.bg1.a1', '144.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3767, -1, 6248, -1, 5529, -1, 4251, -1], 'generators': [3, 100, 144], 'label': '1152.156064.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.bz1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983373
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.b1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.v1.a1', '144.w1.a1', '144.y1.a1', '144.ba1.a1', '144.bd1.a1', '144.bh1.a1', '144.bn1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4053, -1, 5714, -1, 4098, -1, 4085, -1], 'generators': [3, 100, 624], 'label': '1152.156064.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.ca1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983374
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a2', '36.b1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.v1.a1', '144.w1.a1', '144.y1.a1', '144.ba1.a2', '144.bd1.a1', '144.bh1.a2', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4053, -1, 5510, -1, 4098, -1, 4131, -1], 'generators': [99, 100, 624], 'label': '1152.156064.72.ca1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.ca1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983375
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.c1.a1', '36.k1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.v1.a1', '144.y1.a1', '144.bb1.a1', '144.bm1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4580, -1, 5233, -1, 6760, -1, 4867, -1], 'generators': [3, 4, 144], 'label': '1152.156064.72.cb1.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.cb1.a1', 'projective_image': '576.8353', '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: 60983376
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.a1', '24.cr1.a1', '36.m1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.bo1.a1', '144.bq1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9307, -1, 1168, -1, 8188, -1, 7598, -1], 'generators': [1, 2], 'label': '1152.156064.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.cc1.a1', 'projective_image': '576.8353', '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: 60983377
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '96.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '24.bq1.a1', '24.br1.a1', '24.bs1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1408, -1, 8305, -1, 722, -1, 1812, -1], 'generators': [3, 576, 672, 8, 32, 384], 'label': '1152.156064.8.d1.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.d1.a1', 'projective_image': '576.8353', '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': '48.49'}
  • id: 60983378
    {'ambient': '1152.156064', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.a1', '24.cs1.a1', '24.ct1.a1', '36.o1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.b1.a1', '144.bp1.a1', '144.br1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8766, -1, 1654, -1, 8150, -1, 7242, -1], 'generators': [17, 18], 'label': '1152.156064.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cd1.a1', 'projective_image': '576.8353', '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: 60983379
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.b1.a1', '36.j1.a1', '36.p1.a1'], 'contains': ['144.z1.a1', '144.ba1.a1', '144.bd1.a1', '144.bf1.a1', '144.bh1.a2', '144.bj1.a1', '144.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3950, -1, 5548, -1, 4152, -1, 4297, -1], 'generators': [675, 100, 624], 'label': '1152.156064.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.ce1.a1', 'projective_image': '576.8353', '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: 60983380
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a2', '36.b1.a1', '36.j1.a1', '36.p1.a1'], 'contains': ['144.z1.a1', '144.ba1.a2', '144.bd1.a1', '144.bf1.a1', '144.bh1.a1', '144.bj1.a2', '144.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3950, -1, 5773, -1, 4152, -1, 4343, -1], 'generators': [579, 100, 624], 'label': '1152.156064.72.ce1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.ce1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983381
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.c1.a1', '36.p1.a1', '36.bv1.a1'], 'contains': ['144.z1.a1', '144.bb1.a1', '144.bf1.a1', '144.bi1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5232, -1, 5144, -1, 6814, -1, 5024, -1], 'generators': [99, 4, 144], 'label': '1152.156064.72.cf1.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.cf1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983382
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '36.d1.a1', '36.k1.a1', '36.p1.a1'], 'contains': ['144.ba1.a1', '144.ba1.a2', '144.bb1.a1', '144.bh1.a1', '144.bh1.a2', '144.bi1.a1', '144.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6367, -1, 5344, -1, 6652, -1, 4465, -1], 'generators': [579, 4, 144], 'label': '1152.156064.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.cg1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983383
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '36.d1.a1', '36.j1.a1', '36.bw1.a1'], 'contains': ['144.ba1.a2', '144.bc1.a1', '144.bg1.a1', '144.bj1.a1', '144.bn1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5469, -1, 4379, -1, 5857, -1, 5386, -1], 'generators': [675, 100, 144], 'label': '1152.156064.72.ch1.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.ch1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983384
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a2', '36.d1.a1', '36.j1.a1', '36.bw1.a2'], 'contains': ['144.ba1.a1', '144.bc1.a1', '144.bg1.a1', '144.bj1.a2', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5469, -1, 4581, -1, 5857, -1, 5569, -1], 'generators': [579, 100, 144], 'label': '1152.156064.72.ch1.a2', '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.ch1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983385
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '36.f1.a1', '36.bu1.a1', '36.bv1.a1'], 'contains': ['144.bb1.a1', '144.be1.a1', '144.bo1.a1', '144.bp1.a1', '144.bx1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7929, -1, 984, -1, 8235, -1, 7951, -1], 'generators': [1, 4, 720], 'label': '1152.156064.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.ci1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983386
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1.a1', '36.g1.a1', '36.bu1.a1', '36.bv1.a1'], 'contains': ['144.bb1.a1', '144.bq1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9749, -1, 1199, -1, 8625, -1, 7669, -1], 'generators': [2, 720], 'label': '1152.156064.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cj1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983387
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1.a1', '36.f1.a1', '36.bw1.a1', '36.bw1.a2'], 'contains': ['144.bc1.a1', '144.be1.a1', '144.bs1.a1', '144.bt1.a1', '144.bw1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7461, -1, 313, -1, 7801, -1, 9249, -1], 'generators': [1, 676, 720], 'label': '1152.156064.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.ck1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983388
    {'ambient': '1152.156064', '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.c1.a1', '576.f1.a1', '576.c1.b1', '576.f1.b1', '576.h1.a1', '576.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.b1.a1', '6.p1.a1', '8.k1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5930, 3097, 4650, 8634, 2357, 6162, 3546, 6254], 'generators': [1, 8, 32, 2, 4, 576, 672, 384], 'label': '1152.156064.2.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.d1.a1', '4.f1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '576.8353', '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': '192.1488'}
  • id: 60983389
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '288.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.o1.a1', '24.bt1.a1', '24.bu1.a1', '32.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1340, -1, 8248, -1, 578, -1, 1742, -1], 'generators': [51, 384, 576, 8, 32, 672], 'label': '1152.156064.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '576.8353', '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': '144.190'}
  • id: 60983390
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1.a1', '36.h1.a1', '36.bw1.a1', '36.bw1.a2'], 'contains': ['144.bc1.a1', '144.bu1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8347, -1, 559, -1, 7473, -1, 9601, -1], 'generators': [98, 720], 'label': '1152.156064.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cl1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983391
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '36.m1.a1', '36.bs1.a1', '36.bv1.a1'], 'contains': ['144.bi1.a1', '144.bo1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9423, -1, 1117, -1, 8671, -1, 7866, -1], 'generators': [1, 674], 'label': '1152.156064.72.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.cm1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983392
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '36.o1.a1', '36.bs1.a1', '36.bv1.a1'], 'contains': ['144.bi1.a1', '144.bp1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8831, -1, 1274, -1, 8579, -1, 7631, -1], 'generators': [17, 594], 'label': '1152.156064.72.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cn1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983393
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '36.w1.a1', '36.bt1.a1', '36.bw1.a1'], 'contains': ['144.bj1.a1', '144.bs1.a1', '144.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8261, -1, 410, -1, 7557, -1, 9484, -1], 'generators': [1, 578], 'label': '1152.156064.72.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.co1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983394
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a2', '36.w1.a1', '36.bt1.a2', '36.bw1.a2'], 'contains': ['144.bj1.a2', '144.bs1.a1', '144.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8261, -1, 383, -1, 7557, -1, 9517, -1], 'generators': [1, 98], 'label': '1152.156064.72.co1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.co1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983395
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a1', '36.y1.a1', '36.bt1.a1', '36.bw1.a1'], 'contains': ['144.bj1.a1', '144.bt1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7858, -1, 527, -1, 7427, -1, 9288, -1], 'generators': [17, 114], 'label': '1152.156064.72.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cp1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983396
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a2', '36.y1.a1', '36.bt1.a2', '36.bw1.a2'], 'contains': ['144.bj1.a2', '144.bt1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7858, -1, 592, -1, 7427, -1, 9386, -1], 'generators': [17, 690], 'label': '1152.156064.72.cp1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cp1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983397
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1.a1', '24.di1.a1', '36.ba1.a1', '36.br1.a1', '36.bv1.a1'], 'contains': ['144.bl1.a1', '144.bo1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8980, -1, 2045, -1, 8281, -1, 7565, -1], 'generators': [65, 18], 'label': '1152.156064.72.cq1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cq1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983398
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1.a1', '24.dj1.a1', '36.bc1.a1', '36.br1.a1', '36.bv1.a1'], 'contains': ['144.bl1.a1', '144.bp1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8798, -1, 1081, -1, 8320, -1, 7533, -1], 'generators': [49, 2], 'label': '1152.156064.72.cr1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cr1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983399
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1.a1', '36.ba1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.bm1.a1', '144.bo1.a1', '144.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9391, -1, 1247, -1, 8502, -1, 7787, -1], 'generators': [65, 594], 'label': '1152.156064.72.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.cs1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983400
    {'ambient': '1152.156064', '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.d1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.bv1.a1', '24.by1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3576, -1, 5697, -1, 1085, -1, 2761, -1], 'generators': [1, 576, 672, 384, 8, 32], 'label': '1152.156064.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '576.8353', '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: 60983401
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1.a1', '36.bc1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.bm1.a1', '144.bp1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9027, -1, 1016, -1, 8541, -1, 7709, -1], 'generators': [49, 674], 'label': '1152.156064.72.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.ct1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983402
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a1', '36.be1.a1', '36.bt1.a1', '36.bw1.a2'], 'contains': ['144.bn1.a1', '144.bs1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7890, -1, 501, -1, 7388, -1, 9418, -1], 'generators': [65, 114], 'label': '1152.156064.72.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cu1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983403
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a2', '36.be1.a1', '36.bt1.a2', '36.bw1.a1'], 'contains': ['144.bn1.a2', '144.bs1.a1', '144.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7890, -1, 618, -1, 7388, -1, 9321, -1], 'generators': [65, 690], 'label': '1152.156064.72.cu1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cu1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983404
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1.a1', '36.bg1.a1', '36.bt1.a1', '36.bw1.a2'], 'contains': ['144.bn1.a1', '144.bt1.a1', '144.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7768, -1, 208, -1, 7519, -1, 9451, -1], 'generators': [49, 578], 'label': '1152.156064.72.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cv1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983405
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1.a2', '36.bg1.a1', '36.bt1.a2', '36.bw1.a1'], 'contains': ['144.bn1.a2', '144.bt1.a1', '144.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7768, -1, 437, -1, 7519, -1, 9353, -1], 'generators': [49, 98], 'label': '1152.156064.72.cv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cv1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983406
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1.a1', '36.bh1.a1'], 'contains': ['144.by1.a1', '144.bz1.a1', '144.ca1.a1', '144.cb1.a1', '144.cc1.a1', '144.cd1.b1', '144.ce1.b1', '144.ci1.a1', '144.cj1.a1', '144.cl1.a1', '144.cl1.a2', '144.cm1.a1', '144.cm1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1078, -1, 8420, -1, 1608, -1, 849, -1], 'generators': [3, 584, 48, 96], 'label': '1152.156064.72.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cw1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983407
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1.b1', '36.bh1.a1'], 'contains': ['144.by1.b1', '144.bz1.b1', '144.ca1.b1', '144.cb1.a1', '144.cc1.a1', '144.cd1.a1', '144.ce1.a1', '144.ci1.b1', '144.cj1.b1', '144.cl1.a1', '144.cl1.a2', '144.cm1.a1', '144.cm1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1078, -1, 8845, -1, 1608, -1, 821, -1], 'generators': [3, 584, 624, 96], 'label': '1152.156064.72.cw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.cw1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983408
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.a1', '24.dq1.a1', '36.bh1.a1'], 'contains': ['144.bz1.a1', '144.ca1.a1', '144.cd1.a1', '144.ce1.a1', '144.cf1.a1', '144.cg1.a1', '144.ch1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [626, -1, 9475, -1, 737, -1, 448, -1], 'generators': [3, 48, 96, 576], 'label': '1152.156064.72.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '72.cx1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 60983409
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.b1', '24.dq1.b1', '36.bh1.a1'], 'contains': ['144.bz1.b1', '144.ca1.b1', '144.cd1.b1', '144.ce1.b1', '144.cf1.b1', '144.cg1.a1', '144.ch1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [626, -1, 9601, -1, 737, -1, 475, -1], 'generators': [3, 56, 96, 576], 'label': '1152.156064.72.cx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '72.cx1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 60983410
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.c1.a1', '48.g1.a1', '48.y1.a1', '48.z1.a1', '48.ba1.a1', '48.bb1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '288.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2607, 5832, 5373, 3495, 4548, 4843, 3657, 3869], 'generators': [8, 48, 384], 'label': '1152.156064.96.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '192.b1.b1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983411
    {'ambient': '1152.156064', '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.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.bw1.a1', '24.bz1.a1', '24.cb1.a1', '32.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3505, -1, 4853, -1, 1313, -1, 2874, -1], 'generators': [17, 576, 672, 8, 32, 384], 'label': '1152.156064.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.g1.a1', 'projective_image': '576.8353', '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: 60983412
    {'ambient': '1152.156064', 'aut_centralizer_order': 1152, 'aut_label': '96.b1', '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.e1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.m1.a1', '48.bl1.a1', '48.bs1.a1', '48.bw1.a1', '48.by1.a1', '48.bz1.a1', '48.ca1.a1', '48.cb1.a1'], 'contains': ['192.a1.a1', '288.a1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6067, 3675, 3645, 5580, 7630, 6765, 5695, 6242], 'generators': [4, 384, 8], 'label': '1152.156064.96.b1.a1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['24.b1.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.b1.a1', 'projective_image': '576.8353', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983413
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '96.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.c1.a1', '48.o1.a1', '48.bf1.a1', '48.bm1.a1', '48.bq1.a1', '48.cg1.a1'], 'contains': ['192.a1.a1', '288.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4663, 4596, 4091, 4414, 5461, 5353, 4774, 4590], 'generators': [60, 8, 384], 'label': '1152.156064.96.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['24.c1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983414
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.b1.a1', 'complements': ['12.cf1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.f1.a1', '48.f1.b1', '48.cx1.a1', '48.db1.a1'], 'contains': ['192.e1.a1', '288.b1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [398, 8357, 9507, 1155, 784, 3213, 730, 2100], 'generators': [96, 576, 384], 'label': '1152.156064.96.d1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.d1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.f1.b1', '48.f1.a1'], 'normal_contains': ['288.b1.a1', '384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.d1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '12.4', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983415
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '96.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '24.e1.a1', 'complements': ['12.cg1.a1', '12.ch1.a1', '12.ci1.a1', '12.ci1.a2', '12.cj1.a1', '12.ck1.a1', '12.cl1.a1', '12.cl1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.b1.a1', '48.cw1.a1', '48.cw1.b1', '48.cy1.a1', '48.da1.a1'], 'contains': ['288.b1.a1', '384.b1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9, 9040, 9924, 1977, 213, 2566, 290, 2705], 'generators': [32, 96, 576], 'label': '1152.156064.96.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.e1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1'], 'normal_contains': ['288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.e1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.38', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60983416
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '96.f1', '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.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', '48.t1.a1'], 'contains': ['192.a1.a1', '192.e1.a1', '192.g1.a1', '288.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2655, -1, 5060, -1, 3541, -1, 3799, -1], 'generators': [8, 96, 384], 'label': '1152.156064.96.f1.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.f1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983417
    {'ambient': '1152.156064', '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': '24.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '32.b1.a1', '48.v1.a1', '48.w1.a1', '48.x1.a1'], 'contains': ['192.c1.a1', '192.f1.a1', '192.f1.b1', '288.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1414, -1, 8210, -1, 1041, -1, 994, -1], 'generators': [8, 48, 32], 'label': '1152.156064.96.g1.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.g1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983418
    {'ambient': '1152.156064', 'aut_centralizer_order': 576, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.d1.a1', '48.h1.a1', '48.y1.a1', '48.bc1.a1', '48.bd1.a1', '48.bf1.a1', '48.bg1.a1'], 'contains': ['192.a1.a1', '192.h1.a1', '288.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2212, -1, 7515, -1, 3659, -1, 2890, -1], 'generators': [3, 8, 384], 'label': '1152.156064.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.h1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983419
    {'ambient': '1152.156064', 'aut_centralizer_order': 144, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '32.c1.a1', '48.v1.a1', '48.be1.a1', '48.bh1.a1'], 'contains': ['192.c1.a1', '192.i1.a1', '288.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1459, -1, 8133, -1, 987, -1, 2155, -1], 'generators': [3, 8, 32], 'label': '1152.156064.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '96.i1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983420
    {'ambient': '1152.156064', 'aut_centralizer_order': 72, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '32.c1.a1', '48.bi1.a1'], 'contains': ['192.d1.a1', '192.j1.a1', '288.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1637, -1, 8017, -1, 2253, -1, 2294, -1], 'generators': [3, 8, 416], 'label': '1152.156064.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '96.j1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983421
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.i1.a1', '48.bc1.a1', '48.bj1.a1', '48.bk1.a1', '48.bk1.a2', '48.bl1.a1', '48.bm1.a1', '48.bn1.a1', '48.bo1.a1'], 'contains': ['192.a1.a1', '192.k1.a1', '192.k1.b1', '288.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2956, -1, 6569, -1, 3963, -1, 3557, -1], 'generators': [8, 144, 384], 'label': '1152.156064.96.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': '96.k1.a1', 'projective_image': '576.8353', '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': '6.1'}
  • id: 60983422
    {'ambient': '1152.156064', 'aut_centralizer_order': 6, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '192.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.l1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '24.e1.a1', '24.cc1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3812, -1, 6981, -1, 1711, -1, 2584, -1], 'generators': [3, 384, 8, 4, 48, 32], 'label': '1152.156064.8.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': '576.8353', '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': '48.38'}
  • id: 60983423
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.j1.a1', '48.z1.a1', '48.bd1.a1', '48.bj1.a1', '48.bk1.a1', '48.bk1.a2', '48.bp1.a1', '48.bq1.a1', '48.br1.a1', '48.br1.a2', '48.bs1.a1', '48.bt1.a1', '48.bt1.a2'], 'contains': ['192.a1.a1', '192.l1.a1', '288.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2990, -1, 6389, -1, 4004, -1, 3622, -1], 'generators': [99, 8, 384], 'label': '1152.156064.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.l1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983424
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '32.d1.a1', '48.v1.a1', '48.be1.a1', '48.bu1.a1'], 'contains': ['192.c1.a1', '192.m1.a1', '288.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1504, -1, 8085, -1, 934, -1, 2110, -1], 'generators': [51, 8, 32], 'label': '1152.156064.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '96.m1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983425
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.e1.a1', '48.k1.a1', '48.y1.a1', '48.bf1.a1', '48.bj1.a1', '48.bp1.a1', '48.bv1.a1'], 'contains': ['192.a1.a1', '192.n1.a1', '288.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2584, -1, 6944, -1, 3764, -1, 3427, -1], 'generators': [51, 8, 384], 'label': '1152.156064.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.n1.a1', 'projective_image': '576.8353', '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: 60983426
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '96.o1', '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.k1.a1', '48.l1.a1', '48.z1.a1', '48.bc1.a1', '48.bg1.a1', '48.bk1.a1', '48.bk1.a2', '48.bq1.a1', '48.br1.a1', '48.br1.a2', '48.bv1.a1', '48.bw1.a1', '48.bx1.a1', '48.bx1.a2'], 'contains': ['192.a1.a1', '192.o1.a1', '288.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3024, -1, 5487, -1, 3878, -1, 3479, -1], 'generators': [147, 8, 384], 'label': '1152.156064.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.o1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983427
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.n1.a1', '48.ba1.a1', '48.bd1.a1', '48.bm1.a1', '48.bn1.a1', '48.bt1.a1', '48.bt1.a2', '48.bv1.a1', '48.bx1.a1', '48.bx1.a2', '48.cc1.a1', '48.cd1.a1', '48.ce1.a1', '48.cf1.a1'], 'contains': ['192.a1.a1', '288.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5773, -1, 3460, -1, 5982, -1, 5860, -1], 'generators': [100, 384, 8], 'label': '1152.156064.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.p1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983428
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.p1.a1', '48.ba1.a1', '48.bg1.a1', '48.bl1.a1', '48.bn1.a1', '48.bp1.a1', '48.br1.a1', '48.br1.a2', '48.ch1.a1'], 'contains': ['192.a1.a1', '288.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4453, -1, 4126, -1, 4131, -1, 4698, -1], 'generators': [156, 8, 384], 'label': '1152.156064.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.q1.a1', 'projective_image': '576.8353', '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: 60983429
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.r1.a1', '48.bb1.a1', '48.bo1.a1', '48.by1.a1', '48.cc1.a1', '48.cg1.a1', '48.ch1.a1'], 'contains': ['192.a1.a1', '288.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5514, -1, 2533, -1, 6776, -1, 7166, -1], 'generators': [1, 384, 8], 'label': '1152.156064.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '96.r1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983430
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '48.t1.a1', '48.bb1.a1', '48.bo1.a1', '48.bz1.a1', '48.cd1.a1', '48.cg1.a1', '48.ch1.a1'], 'contains': ['192.a1.a1', '288.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5422, -1, 2508, -1, 6741, -1, 7136, -1], 'generators': [17, 8, 384], 'label': '1152.156064.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '96.s1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983431
    {'ambient': '1152.156064', 'aut_centralizer_order': 288, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '32.e1.a1', '48.w1.a1', '48.bh1.a1', '48.bu1.a1', '48.ci1.a1', '48.cj1.a1', '48.ck1.a1', '48.cl1.a1'], 'contains': ['192.c1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4768, -1, 5950, -1, 2414, -1, 3357, -1], 'generators': [4, 32, 8], 'label': '1152.156064.96.t1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '96.t1.a1', 'projective_image': '576.8353', '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: 60983432
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '32.f1.a1', '48.w1.a1', '48.be1.a1', '48.cm1.a1'], 'contains': ['192.c1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3536, -1, 6057, -1, 1138, -1, 2446, -1], 'generators': [60, 32, 8], 'label': '1152.156064.96.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': '576.8353', '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': '4.2'}
  • id: 60983433
    {'ambient': '1152.156064', '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.e1.a1', '16.i1.a1', '16.j1.a1', '16.m1.a1', '24.cd1.a1', '24.ci1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4211, -1, 5099, -1, 2005, -1, 3050, -1], 'generators': [1, 384, 32, 4, 48, 8], 'label': '1152.156064.8.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': '576.8353', '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': '144.153'}
  • id: 60983434
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1.a1', '32.g1.a1', '48.x1.a1', '48.ci1.a1', '48.cm1.a1'], 'contains': ['192.c1.a1', '288.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4193, -1, 5091, -1, 1183, -1, 3038, -1], 'generators': [1, 8, 32], 'label': '1152.156064.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '96.v1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983435
    {'ambient': '1152.156064', '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.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '32.h1.a1', '48.x1.a1', '48.cj1.a1', '48.cm1.a1'], 'contains': ['192.c1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3902, -1, 4851, -1, 1503, -1, 3068, -1], 'generators': [17, 8, 32], 'label': '1152.156064.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '96.w1.a1', 'projective_image': '576.8353', '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: 60983436
    {'ambient': '1152.156064', 'aut_centralizer_order': 144, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '32.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '32.e1.a1', '48.bi1.a1', '48.cn1.a1', '48.co1.a1'], 'contains': ['192.d1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4834, -1, 5144, -1, 5397, -1, 3684, -1], 'generators': [4, 416, 8], 'label': '1152.156064.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1.a1', 'old_label': '96.x1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983437
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '32.h1.a1', '48.cn1.a1'], 'contains': ['192.d1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4223, -1, 4555, -1, 2345, -1, 3584, -1], 'generators': [17, 8, 416], 'label': '1152.156064.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cn1.a1', 'old_label': '96.y1.a1', 'projective_image': '576.8353', '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': '12.4'}
  • id: 60983438
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.g1.a1', '48.cp1.a1', '48.cq1.a1', '48.cr1.a1'], 'contains': ['192.b1.a1', '192.e1.a1', '192.k1.a1', '288.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [458, -1, 7136, -1, 1471, -1, 1300, -1], 'generators': [48, 96, 384], 'label': '1152.156064.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.z1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983439
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.g1.a1', '48.cp1.b1', '48.cq1.b1', '48.cr1.b1'], 'contains': ['192.b1.b1', '192.e1.a1', '192.k1.b1', '288.o1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [458, -1, 9044, -1, 1471, -1, 1348, -1], 'generators': [56, 96, 384], 'label': '1152.156064.96.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.z1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983440
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.cp1.a1', '48.cp1.b1', '48.cs1.a1', '48.ct1.a1'], 'contains': ['192.e1.a1', '192.g1.a1', '288.p1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [960, -1, 8738, -1, 1645, -1, 1383, -1], 'generators': [584, 96, 384], 'label': '1152.156064.96.ba1.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.ba1.a1', 'projective_image': '1152.156064', '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': '4.2'}
  • id: 60983441
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.cq1.a1', '48.cq1.b1', '48.cs1.a1', '48.cu1.a1', '48.cu1.b1', '48.cx1.a1'], 'contains': ['192.e1.a1', '192.h1.a1', '192.l1.a1', '288.q1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [537, -1, 9114, -1, 1309, -1, 1239, -1], 'generators': [3, 96, 384], 'label': '1152.156064.96.bb1.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': '96.bb1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983442
    {'ambient': '1152.156064', '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': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.i1.a1', '48.cp1.b1', '48.cu1.a1', '48.cv1.a1'], 'contains': ['192.e1.a1', '192.k1.a1', '288.r1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [798, -1, 9084, -1, 1411, -1, 1029, -1], 'generators': [624, 96, 384], 'label': '1152.156064.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bc1.a1', 'projective_image': '1152.156064', '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: 60983443
    {'ambient': '1152.156064', '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': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.i1.a1', '48.cp1.a1', '48.cu1.b1', '48.cv1.b1'], 'contains': ['192.e1.a1', '192.k1.b1', '288.r1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [798, -1, 9189, -1, 1411, -1, 1204, -1], 'generators': [632, 96, 384], 'label': '1152.156064.96.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bc1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983444
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '8.j1', '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.c1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.l1.a1', '24.ce1.a1', '24.cj1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7113, -1, 4058, -1, 2679, -1, 4413, -1], 'generators': [2, 384, 32, 48, 4, 8], 'label': '1152.156064.8.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': '576.8353', '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': '72.46'}
  • id: 60983445
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.cr1.a1', '48.cr1.b1', '48.cs1.a1', '48.cv1.a1', '48.cv1.b1', '48.cx1.a1'], 'contains': ['192.e1.a1', '192.l1.a1', '288.s1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [492, -1, 9150, -1, 1256, -1, 1087, -1], 'generators': [579, 96, 384], 'label': '1152.156064.96.bd1.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': '96.bd1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983446
    {'ambient': '1152.156064', '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.k1.a1', '48.cq1.a1', '48.cq1.b1', '48.ct1.a1', '48.cv1.a1', '48.cv1.b1', '48.db1.a1'], 'contains': ['192.e1.a1', '192.n1.a1', '192.o1.a1', '288.t1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [889, -1, 9025, -1, 1350, -1, 1324, -1], 'generators': [51, 96, 384], 'label': '1152.156064.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.be1.a1', 'projective_image': '1152.156064', '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: 60983447
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.cr1.a1', '48.cr1.b1', '48.ct1.a1', '48.cu1.a1', '48.cu1.b1', '48.db1.a1'], 'contains': ['192.e1.a1', '192.o1.a1', '288.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [708, -1, 9209, -1, 1215, -1, 1053, -1], 'generators': [627, 96, 384], 'label': '1152.156064.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bf1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983448
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.u1.a1', '48.cz1.a1'], 'contains': ['288.b1.a1', '384.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [136, -1, 9874, -1, 728, -1, 253, -1], 'generators': [416, 96, 576], 'label': '1152.156064.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '96.bg1.a1', 'projective_image': '1152.156064', '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': '24.12'}
  • id: 60983449
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.a1', '32.i1.a1', '48.v1.a1'], 'contains': ['192.f1.a1', '192.i1.a1', '192.m1.a1', '288.w1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [195, -1, 9762, -1, 482, -1, 324, -1], 'generators': [3, 48, 32], 'label': '1152.156064.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.v1.a1', 'old_label': '96.bh1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983450
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.b1', '32.i1.b1', '48.v1.a1'], 'contains': ['192.f1.b1', '192.i1.a1', '192.m1.a1', '288.w1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [195, -1, 9724, -1, 482, -1, 427, -1], 'generators': [3, 56, 32], 'label': '1152.156064.96.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.v1.a1', 'old_label': '96.bh1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983451
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.cp1.a1', '48.dc1.a1', '48.dd1.a1', '48.de1.a1'], 'contains': ['192.b1.a1', '192.g1.a1', '192.k1.b1', '288.v1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1964, -1, 6599, -1, 2212, -1, 2214, -1], 'generators': [104, 48, 384], 'label': '1152.156064.96.bi1.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.bi1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983452
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.cp1.b1', '48.dc1.b1', '48.dd1.b1', '48.de1.b1'], 'contains': ['192.b1.b1', '192.g1.a1', '192.k1.a1', '288.v1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1964, -1, 6630, -1, 2212, -1, 2190, -1], 'generators': [104, 144, 384], 'label': '1152.156064.96.bi1.b1', '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.bi1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983453
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '24.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '48.y1.a1', '48.cq1.a1', '48.dc1.a1'], 'contains': ['192.b1.a1', '192.h1.a1', '192.n1.a1', '288.w1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [853, -1, 8524, -1, 1750, -1, 1828, -1], 'generators': [3, 48, 384], 'label': '1152.156064.96.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.bj1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983454
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '24.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '48.y1.a1', '48.cq1.b1', '48.dc1.b1'], 'contains': ['192.b1.b1', '192.h1.a1', '192.n1.a1', '288.w1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [853, -1, 8565, -1, 1750, -1, 1852, -1], 'generators': [3, 56, 384], 'label': '1152.156064.96.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.bj1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983455
    {'ambient': '1152.156064', '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.g1.a1', '16.i1.a1', '16.k1.a1', '24.cp1.a1', '24.cr1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5965, -1, 4693, -1, 2407, -1, 3606, -1], 'generators': [1, 32, 8, 2, 384, 4], 'label': '1152.156064.8.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': '576.8353', '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': '48.43'}
  • id: 60983456
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '48.cq1.a1', '48.cr1.a1', '48.dc1.a1', '48.dd1.a1'], 'contains': ['192.b1.a1', '192.l1.a1', '192.o1.a1', '288.x1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1550, -1, 7186, -1, 1807, -1, 1945, -1], 'generators': [99, 48, 384], 'label': '1152.156064.96.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bk1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983457
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '48.cq1.b1', '48.cr1.b1', '48.dc1.b1', '48.dd1.b1'], 'contains': ['192.b1.b1', '192.l1.a1', '192.o1.a1', '288.x1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1550, -1, 7339, -1, 1807, -1, 1969, -1], 'generators': [99, 56, 384], 'label': '1152.156064.96.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bk1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983458
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.cs1.a1', '48.dc1.a1', '48.dc1.b1', '48.df1.a1', '48.df1.a2'], 'contains': ['192.g1.a1', '192.h1.a1', '192.l1.a1', '288.y1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1698, -1, 8486, -1, 1904, -1, 1911, -1], 'generators': [3, 104, 384], 'label': '1152.156064.96.bl1.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': '96.bl1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983459
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.cp1.a1', '48.cp1.b1', '48.df1.a1', '48.df1.a2', '48.dg1.a1', '48.dg1.a2'], 'contains': ['192.g1.a1', '192.k1.a1', '192.k1.b1', '288.z1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2059, -1, 7106, -1, 2184, -1, 1780, -1], 'generators': [104, 624, 384], 'label': '1152.156064.96.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.bm1.a1', 'projective_image': '1152.156064', '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': '6.1'}
  • id: 60983460
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.cs1.a1', '48.dd1.a1', '48.dd1.b1', '48.dg1.a1', '48.dg1.a2'], 'contains': ['192.g1.a1', '192.l1.a1', '288.ba1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1997, -1, 6904, -1, 2079, -1, 2065, -1], 'generators': [579, 104, 384], 'label': '1152.156064.96.bn1.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': '96.bn1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983461
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '96.bo1', '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.k1.a1', '48.ct1.a1', '48.dc1.a1', '48.dc1.b1', '48.dg1.a1', '48.dg1.a2'], 'contains': ['192.g1.a1', '192.n1.a1', '192.o1.a1', '288.bb1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1856, -1, 7988, -1, 1945, -1, 1993, -1], 'generators': [51, 104, 384], 'label': '1152.156064.96.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bo1.a1', 'projective_image': '1152.156064', '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: 60983462
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.ct1.a1', '48.dd1.a1', '48.dd1.b1', '48.df1.a1', '48.df1.a2'], 'contains': ['192.g1.a1', '192.o1.a1', '288.bc1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2032, -1, 6874, -1, 2038, -1, 2030, -1], 'generators': [627, 104, 384], 'label': '1152.156064.96.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bp1.a1', 'projective_image': '1152.156064', '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: 60983463
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.de1.a1', '48.de1.b1'], 'contains': ['192.g1.a1', '288.bd1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3345, -1, 4974, -1, 4402, -1, 5544, -1], 'generators': [97, 384, 680], 'label': '1152.156064.96.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.bq1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983464
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.de1.a1', '48.de1.b1'], 'contains': ['192.g1.a1', '288.be1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3278, -1, 4887, -1, 4367, -1, 5620, -1], 'generators': [113, 584, 384], 'label': '1152.156064.96.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.br1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60983465
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '48.cq1.a1', '48.cu1.a1', '48.dc1.b1', '48.df1.a1', '48.df1.a2'], 'contains': ['192.h1.a1', '192.k1.a1', '192.o1.a1', '288.bf1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1803, -1, 7595, -1, 1779, -1, 1636, -1], 'generators': [3, 144, 384], 'label': '1152.156064.96.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bs1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983466
    {'ambient': '1152.156064', '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.g1.a1', '16.j1.a1', '16.l1.a1', '24.cq1.a1', '24.cs1.a1', '24.ct1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5578, -1, 4450, -1, 2966, -1, 3527, -1], 'generators': [17, 384, 32, 18, 4, 8], 'label': '1152.156064.8.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': '576.8353', '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': '144.153'}
  • id: 60983581
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.da1.a1', '64.d1.a1', '96.m1.a1', '96.bh1.a1', '96.bh1.b1'], 'contains': ['384.b1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [268, -1, 9721, -1, 578, -1, 473, -1], 'generators': [51, 32], 'label': '1152.156064.192.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.v1.a1', 'old_label': '192.m1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983467
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '48.cq1.b1', '48.cu1.b1', '48.dc1.a1', '48.df1.a1', '48.df1.a2'], 'contains': ['192.h1.a1', '192.k1.b1', '192.o1.a1', '288.bf1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1803, -1, 8260, -1, 1779, -1, 1708, -1], 'generators': [3, 152, 384], 'label': '1152.156064.96.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bs1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983468
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '48.cq1.a1', '48.cv1.a1', '48.dc1.b1', '48.dg1.a1', '48.dg1.a2'], 'contains': ['192.k1.a1', '192.l1.a1', '192.n1.a1', '288.bg1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1581, -1, 7634, -1, 1863, -1, 1804, -1], 'generators': [99, 144, 384], 'label': '1152.156064.96.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bt1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983469
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '48.cq1.b1', '48.cv1.b1', '48.dc1.a1', '48.dg1.a1', '48.dg1.a2'], 'contains': ['192.k1.b1', '192.l1.a1', '192.n1.a1', '288.bg1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1581, -1, 8161, -1, 1863, -1, 1876, -1], 'generators': [99, 152, 384], 'label': '1152.156064.96.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bt1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983470
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a1', '48.cr1.a1', '48.cu1.a1', '48.cv1.a1', '48.dd1.b1', '48.df1.a2', '48.dg1.a2'], 'contains': ['192.k1.a1', '192.l1.a1', '192.o1.a1', '288.bh1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 7206, -1, 1835, -1, 1684, -1], 'generators': [579, 144, 384], 'label': '1152.156064.96.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bu1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983471
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a2', '48.cr1.a1', '48.cu1.a1', '48.cv1.a1', '48.dd1.b1', '48.df1.a1', '48.dg1.a1'], 'contains': ['192.k1.a1', '192.l1.a1', '192.o1.a1', '288.bh1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 7167, -1, 1835, -1, 1660, -1], 'generators': [675, 144, 384], 'label': '1152.156064.96.bu1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bu1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983472
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a1', '48.cr1.b1', '48.cu1.b1', '48.cv1.b1', '48.dd1.a1', '48.df1.a1', '48.dg1.a1'], 'contains': ['192.k1.b1', '192.l1.a1', '192.o1.a1', '288.bh1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 7737, -1, 1835, -1, 1732, -1], 'generators': [579, 152, 384], 'label': '1152.156064.96.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bu1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983473
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a2', '48.cr1.b1', '48.cu1.b1', '48.cv1.b1', '48.dd1.a1', '48.df1.a2', '48.dg1.a2'], 'contains': ['192.k1.b1', '192.l1.a1', '192.o1.a1', '288.bh1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1733, -1, 7615, -1, 1835, -1, 1756, -1], 'generators': [675, 152, 384], 'label': '1152.156064.96.bu1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '96.bu1.b2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983474
    {'ambient': '1152.156064', '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.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '64.a1.a1', '64.b1.a1', '64.b1.b1', '64.c1.a1', '64.d1.a1'], 'contains': ['384.a1.a1', '384.b1.a1', '384.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [96, -1, 9897, -1, 677, -1, 529, -1], 'generators': [32, 384], 'label': '1152.156064.128.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': '1152.156064', '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: 60983475
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '144.a1', 'aut_quo_index': 2, '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.u1.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.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1163, 6765, 8525, 3132, 2311, 4128, 2343, 3421], 'generators': [8, 96, 576], 'label': '1152.156064.144.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': '576.8353', 'quotient_action_image': '6.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983476
    {'ambient': '1152.156064', 'aut_centralizer_order': 576, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.bh1.a1', '48.bi1.a1', '72.l1.a1', '72.bs1.a1', '72.cb1.a1', '72.cc1.a1', '72.cd1.a1'], 'contains': ['288.a1.a1', '288.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4496, 2703, 6007, 7479, 6570, 7487, 4802, 6940], 'generators': [3, 4], 'label': '1152.156064.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.a1.a1', '48.d1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983477
    {'ambient': '1152.156064', '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.h1.a1', '16.i1.a1', '16.l1.a1', '24.dg1.a1', '24.di1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5126, -1, 4772, -1, 2334, -1, 3471, -1], 'generators': [1, 384, 32, 18, 12, 8], 'label': '1152.156064.8.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': '576.8353', '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': '144.153'}
  • id: 60983478
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.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.f1.a1', '288.o1.a1', '288.o1.b1', '288.v1.a1', '288.v1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3391, -1, 5958, -1, 3584, -1, 3531, -1], 'generators': [8, 48, 96], 'label': '1152.156064.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '576.8353', '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': '1.1'}
  • id: 60983479
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.b1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.bm1.a1'], 'contains': ['288.c1.a1', '288.e1.a1', '288.g1.a1', '288.q1.a1', '288.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2308, -1, 7651, -1, 3078, -1, 2854, -1], 'generators': [3, 8, 96], 'label': '1152.156064.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983480
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.h1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.bl1.a1'], 'contains': ['288.c1.a1', '288.f1.a1', '288.r1.a1', '288.r1.b1', '288.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3978, -1, 7427, -1, 3384, -1, 3009, -1], 'generators': [8, 624, 96], 'label': '1152.156064.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983481
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '72.c1.a1', '72.k1.a1', '72.m1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1', '72.bm1.a1'], 'contains': ['288.c1.a1', '288.g1.a1', '288.s1.a1', '288.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3015, -1, 6355, -1, 2963, -1, 3329, -1], 'generators': [579, 8, 96], 'label': '1152.156064.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983482
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.g1', '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.k1.a1', '72.b1.a1', '72.i1.a1', '72.m1.a1', '72.r1.a1', '72.u1.a1', '72.v1.a1', '72.bn1.a1'], 'contains': ['288.c1.a1', '288.h1.a1', '288.i1.a1', '288.t1.a1', '288.bb1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2767, -1, 7077, -1, 3132, -1, 3274, -1], 'generators': [51, 8, 96], 'label': '1152.156064.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.g1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983483
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '72.c1.a1', '72.h1.a1', '72.j1.a1', '72.s1.a1', '72.u1.a1', '72.w1.a1', '72.bn1.a1'], 'contains': ['288.c1.a1', '288.i1.a1', '288.u1.a1', '288.bc1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3187, -1, 6251, -1, 2847, -1, 3301, -1], 'generators': [627, 8, 96], 'label': '1152.156064.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.h1.a1', 'projective_image': '576.8353', '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: 60983484
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '72.a1.a1', '72.d1.a1', '72.l1.a1', '72.n1.a1', '72.t1.a1', '72.v1.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'], 'contains': ['288.a1.a1', '288.c1.a1', '288.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6996, -1, 2851, -1, 6294, -1, 6727, -1], 'generators': [4, 96], 'label': '1152.156064.144.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': '576.8353', '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': '2.1'}
  • id: 60983485
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '72.a1.a1', '72.e1.a1', '72.k1.a1', '72.o1.a1', '72.u1.a1', '72.bf1.a1', '72.bg1.a1'], 'contains': ['288.c1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5799, -1, 3513, -1, 4322, -1, 5777, -1], 'generators': [580, 96], 'label': '1152.156064.144.j1.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.j1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983486
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.d1.a1', '72.i1.a1', '72.o1.a1', '72.s1.a1', '72.bh1.a1', '72.bi1.a1', '72.bo1.a1'], 'contains': ['288.c1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4950, -1, 3950, -1, 4086, -1, 4881, -1], 'generators': [60, 96], 'label': '1152.156064.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.k1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983487
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '72.e1.a1', '72.j1.a1', '72.n1.a1', '72.r1.a1', '72.bj1.a1', '72.bk1.a1', '72.bo1.a1'], 'contains': ['288.c1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4861, -1, 4026, -1, 3838, -1, 4836, -1], 'generators': [636, 96], 'label': '1152.156064.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.l1.a1', 'projective_image': '576.8353', '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: 60983488
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '8.n1', '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.g1.a1', '4.l1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.k1.a1', '24.dh1.a1', '24.dj1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5196, -1, 4299, -1, 2595, -1, 3299, -1], 'generators': [17, 384, 32, 2, 12, 8], 'label': '1152.156064.8.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': '576.8353', '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': '144.153'}
  • id: 60983489
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '72.f1.a1', '72.p1.a1', '72.x1.a1', '72.bf1.a1', '72.bh1.a1', '72.bj1.a1', '72.bp1.a1'], 'contains': ['288.c1.a1', '288.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4906, -1, 4223, -1, 4782, -1, 6453, -1], 'generators': [577, 672], 'label': '1152.156064.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '144.m1.a1', 'projective_image': '576.8353', '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: 60983490
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '72.g1.a1', '72.q1.a1', '72.y1.a1', '72.bf1.a1', '72.bi1.a1', '72.bk1.a1', '72.bp1.a1'], 'contains': ['288.c1.a1', '288.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5944, -1, 2887, -1, 5106, -1, 6863, -1], 'generators': [1, 672], 'label': '1152.156064.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '144.n1.a1', 'projective_image': '576.8353', '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: 60983491
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '72.f1.a1', '72.q1.a1', '72.z1.a1', '72.bg1.a1', '72.bh1.a1', '72.bk1.a1', '72.bq1.a1'], 'contains': ['288.c1.a1', '288.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4816, -1, 4179, -1, 4729, -1, 6524, -1], 'generators': [113, 576], 'label': '1152.156064.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '144.o1.a1', 'projective_image': '576.8353', '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: 60983492
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.p1', '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.t1.a1', '72.g1.a1', '72.p1.a1', '72.ba1.a1', '72.bg1.a1', '72.bi1.a1', '72.bj1.a1', '72.bq1.a1'], 'contains': ['288.c1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5845, -1, 2539, -1, 5165, -1, 6682, -1], 'generators': [17, 576], 'label': '1152.156064.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '144.p1.a1', 'projective_image': '576.8353', '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: 60983493
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '48.y1.a1', '72.b1.a1', '72.br1.a1', '72.bs1.a1'], 'contains': ['288.d1.a1', '288.e1.a1', '288.h1.a1', '288.w1.a1', '288.w1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2343, -1, 7725, -1, 3616, -1, 2663, -1], 'generators': [3, 8, 48], 'label': '1152.156064.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.q1.a1', 'projective_image': '576.8353', '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: 60983494
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '72.b1.a1', '72.c1.a1', '72.br1.a1', '72.bt1.a1', '72.bu1.a1', '72.bu1.a2'], 'contains': ['288.d1.a1', '288.g1.a1', '288.i1.a1', '288.x1.a1', '288.x1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3230, -1, 6168, -1, 4518, -1, 3504, -1], 'generators': [99, 8, 48], 'label': '1152.156064.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.r1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983495
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.w1.a1', '72.d1.a1', '72.bs1.a1', '72.bt1.a1', '72.bv1.a1', '72.bw1.a1'], 'contains': ['288.a1.a1', '288.d1.a1', '288.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6511, -1, 3749, -1, 6611, -1, 5732, -1], 'generators': [4, 48], 'label': '1152.156064.144.s1.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.s1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983496
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '72.d1.a1', '72.e1.a1', '72.br1.a1', '72.bu1.a1', '72.bu1.a2', '72.bx1.a1', '72.by1.a1'], 'contains': ['288.d1.a1', '288.j1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5988, -1, 3680, -1, 5885, -1, 5897, -1], 'generators': [100, 48], 'label': '1152.156064.144.t1.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.t1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983497
    {'ambient': '1152.156064', '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.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '48.bb1.a1', '72.g1.a1', '72.bv1.a1', '72.bx1.a1'], 'contains': ['288.d1.a1', '288.m1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6638, -1, 2345, -1, 6501, -1, 7227, -1], 'generators': [1, 48], 'label': '1152.156064.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '144.u1.a1', 'projective_image': '576.8353', '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: 60983498
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '72.b1.a1', '72.h1.a1', '72.bz1.a1', '72.ca1.a1', '72.ca1.a2', '72.cb1.a1'], 'contains': ['288.e1.a1', '288.f1.a1', '288.i1.a1', '288.bf1.a1', '288.bf1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2658, -1, 7502, -1, 3702, -1, 2927, -1], 'generators': [3, 8, 144], 'label': '1152.156064.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.v1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983515
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a2', '72.j1.a1', '72.r1.a1', '72.s1.a1', '72.bu1.a2', '72.ca1.a2', '72.ce1.a1', '72.cg1.a1'], 'contains': ['288.g1.a1', '288.i1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3917, -1, 5434, -1, 3935, -1, 4066, -1], 'generators': [579, 156], 'label': '1152.156064.144.bh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bh1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60983499
    {'ambient': '1152.156064', '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.c1.a1', '576.f1.a1', '576.c1.b1', '576.f1.b1', '576.h1.a1', '576.i1.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', '6.s1.a1', '8.l1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5867, 5135, 4455, 5157, 2585, 3132, 3484, 4450], 'generators': [17, 32, 384, 18, 8, 576, 672, 4], 'label': '1152.156064.2.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': '576.8353', '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': '576.8353'}
  • id: 60983500
    {'ambient': '1152.156064', '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': '288.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.a1', '16.n1.a1', '16.o1.a1', '24.dp1.a1', '24.dq1.a1', '32.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [369, -1, 9752, -1, 266, -1, 355, -1], 'generators': [3, 384, 576, 48, 32, 672], 'label': '1152.156064.8.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': '1152.156064', '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': '72.44'}
  • id: 60983501
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1.a1', '72.k1.a1', '72.l1.a1', '72.br1.a1', '72.bz1.a1', '72.ca1.a1', '72.ca1.a2'], 'contains': ['288.e1.a1', '288.g1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3694, -1, 6077, -1, 4988, -1, 4120, -1], 'generators': [3, 100], 'label': '1152.156064.144.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983502
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1.a1', '48.bf1.a1', '72.i1.a1', '72.bs1.a1', '72.bz1.a1'], 'contains': ['288.e1.a1', '288.h1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3043, -1, 6793, -1, 4487, -1, 3725, -1], 'generators': [3, 60], 'label': '1152.156064.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.x1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983503
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.y1', '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.bg1.a1', '72.i1.a1', '72.j1.a1', '72.br1.a1', '72.ca1.a1', '72.ca1.a2', '72.cb1.a1'], 'contains': ['288.e1.a1', '288.i1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3940, -1, 5573, -1, 3907, -1, 3764, -1], 'generators': [3, 156], 'label': '1152.156064.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.y1.a1', 'projective_image': '576.8353', '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: 60983504
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '72.b1.a1', '72.m1.a1', '72.bz1.a1', '72.ce1.a1', '72.ce1.a2', '72.cf1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.h1.a1', '288.bg1.a1', '288.bg1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3077, -1, 7033, -1, 3795, -1, 3453, -1], 'generators': [99, 8, 144], 'label': '1152.156064.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.z1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983505
    {'ambient': '1152.156064', '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': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a1', '72.c1.a1', '72.h1.a1', '72.m1.a1', '72.ca1.a1', '72.ce1.a1', '72.cg1.a1', '72.ch1.a2'], 'contains': ['288.f1.a1', '288.g1.a1', '288.i1.a1', '288.bh1.a1', '288.bh1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3305, -1, 6750, -1, 3734, -1, 2954, -1], 'generators': [579, 8, 144], 'label': '1152.156064.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.ba1.a1', 'projective_image': '576.8353', '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: 60983506
    {'ambient': '1152.156064', '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': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a2', '72.c1.a1', '72.h1.a1', '72.m1.a1', '72.ca1.a2', '72.ce1.a2', '72.cg1.a1', '72.ch1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.i1.a1', '288.bh1.a2', '288.bh1.b2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3305, -1, 6772, -1, 3734, -1, 2982, -1], 'generators': [675, 8, 144], 'label': '1152.156064.144.ba1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.ba1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983507
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.a1', '72.d1.a1', '72.n1.a1', '72.cb1.a1', '72.cf1.a1', '72.cg1.a1', '72.ci1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '288.f1.a1', '288.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6349, -1, 3818, -1, 6820, -1, 5823, -1], 'generators': [4, 144], 'label': '1152.156064.144.bb1.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.bb1.a1', 'projective_image': '576.8353', '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: 60983508
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '72.d1.a1', '72.o1.a1', '72.bz1.a1', '72.ch1.a1', '72.ch1.a2', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.f1.a1', '288.j1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6041, -1, 3475, -1, 5939, -1, 5943, -1], 'generators': [100, 144], 'label': '1152.156064.144.bc1.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.bc1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983509
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '72.e1.a1', '72.n1.a1', '72.o1.a1', '72.ca1.a1', '72.ca1.a2', '72.ce1.a1', '72.ce1.a2'], 'contains': ['288.f1.a1', '288.j1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4994, -1, 4131, -1, 4210, -1, 4736, -1], 'generators': [100, 624], 'label': '1152.156064.144.bd1.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.bd1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983510
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '72.g1.a1', '72.ci1.a1', '72.ck1.a1'], 'contains': ['288.f1.a1', '288.m1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6722, -1, 1838, -1, 7149, -1, 7531, -1], 'generators': [1, 720], 'label': '1152.156064.144.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '144.be1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983511
    {'ambient': '1152.156064', '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': '288.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.b1', '16.n1.a1', '16.o1.a1', '24.dp1.b1', '24.dq1.b1', '32.i1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [369, -1, 9537, -1, 266, -1, 428, -1], 'generators': [3, 384, 576, 56, 32, 672], 'label': '1152.156064.8.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.o1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 60983512
    {'ambient': '1152.156064', '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.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.i1.a1', '72.r1.a1', '72.br1.a1', '72.ce1.a1', '72.ce1.a2', '72.cf1.a1'], 'contains': ['288.g1.a1', '288.h1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3465, -1, 6220, -1, 4045, -1, 3962, -1], 'generators': [99, 156], 'label': '1152.156064.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bf1.a1', 'projective_image': '576.8353', '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: 60983513
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bg1', '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.bq1.a1', '72.i1.a1', '72.s1.a1', '72.bt1.a1', '72.bz1.a1', '72.ch1.a1', '72.ch1.a2'], 'contains': ['288.g1.a1', '288.i1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4004, -1, 5249, -1, 5429, -1, 4328, -1], 'generators': [99, 60], 'label': '1152.156064.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bg1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983514
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '72.j1.a1', '72.r1.a1', '72.s1.a1', '72.bu1.a1', '72.ca1.a1', '72.ce1.a2', '72.cg1.a1'], 'contains': ['288.g1.a1', '288.i1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3917, -1, 5827, -1, 3935, -1, 4090, -1], 'generators': [675, 156], 'label': '1152.156064.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bh1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983516
    {'ambient': '1152.156064', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.l1.a1', '72.t1.a1', '72.bt1.a1', '72.cf1.a1', '72.cg1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.a1.a1', '288.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6286, -1, 4709, -1, 7190, -1, 5230, -1], 'generators': [99, 4], 'label': '1152.156064.144.bi1.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.bi1.a1', 'projective_image': '576.8353', '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: 60983517
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.k1.a1', '72.t1.a1', '72.bu1.a1', '72.ce1.a1', '72.ch1.a1', '72.co1.a1', '72.cp1.a1'], 'contains': ['288.g1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5598, -1, 4481, -1, 5844, -1, 5483, -1], 'generators': [675, 100], 'label': '1152.156064.144.bj1.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.bj1.a1', 'projective_image': '576.8353', '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: 60983518
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a2', '72.k1.a1', '72.t1.a1', '72.bu1.a2', '72.ce1.a2', '72.ch1.a2', '72.co1.a2', '72.cp1.a2'], 'contains': ['288.g1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5598, -1, 4610, -1, 5844, -1, 5518, -1], 'generators': [579, 100], 'label': '1152.156064.144.bj1.a2', '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.bj1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983519
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bk1', '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.bv1.a1', '72.u1.a1', '72.v1.a1', '72.br1.a1', '72.bz1.a1', '72.ce1.a1', '72.ce1.a2'], 'contains': ['288.h1.a1', '288.i1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4090, -1, 5321, -1, 5206, -1, 4274, -1], 'generators': [51, 100], 'label': '1152.156064.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bk1.a1', 'projective_image': '576.8353', '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: 60983520
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.bu1.a1', '72.v1.a1', '72.bs1.a1', '72.cf1.a1', '72.cq1.a1', '72.cr1.a1'], 'contains': ['288.a1.a1', '288.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5351, -1, 5116, -1, 6652, -1, 5024, -1], 'generators': [51, 4], 'label': '1152.156064.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.bl1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983521
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '72.v1.a1', '72.w1.a1', '72.bt1.a1', '72.cb1.a1', '72.cg1.a1', '72.cs1.a1', '72.ct1.a1'], 'contains': ['288.a1.a1', '288.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6399, -1, 4272, -1, 6861, -1, 5201, -1], 'generators': [147, 4], 'label': '1152.156064.144.bm1.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.bm1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983522
    {'ambient': '1152.156064', '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': '144.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': [8136, -1, 2568, -1, 6170, -1, 6851, -1], 'generators': [1, 2, 48, 576], 'label': '1152.156064.9.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': '576.8353', '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': '16.11'}
  • id: 60983523
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.u1.a1', '72.w1.a1', '72.bu1.a1', '72.ca1.a2', '72.ch1.a2', '72.cu1.a1', '72.cv1.a1'], 'contains': ['288.i1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5690, -1, 3899, -1, 5816, -1, 5459, -1], 'generators': [723, 100], 'label': '1152.156064.144.bn1.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.bn1.a1', 'projective_image': '576.8353', '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: 60983524
    {'ambient': '1152.156064', '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': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a2', '72.u1.a1', '72.w1.a1', '72.bu1.a2', '72.ca1.a1', '72.ch1.a1', '72.cu1.a2', '72.cv1.a2'], 'contains': ['288.i1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5690, -1, 3847, -1, 5816, -1, 5364, -1], 'generators': [627, 100], 'label': '1152.156064.144.bn1.a2', '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.bn1.a2', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60983525
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '48.ci1.a1', '72.y1.a1', '72.bv1.a1', '72.cc1.a1', '72.ci1.a1', '72.cm1.a1', '72.cq1.a1', '72.cs1.a1'], 'contains': ['288.a1.a1', '288.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8033, -1, 2013, -1, 8188, -1, 7496, -1], 'generators': [1, 4], 'label': '1152.156064.144.bo1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.bo1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983526
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1.a1', '48.cj1.a1', '48.cn1.a1', '72.ba1.a1', '72.bv1.a1', '72.cd1.a1', '72.ci1.a1', '72.cn1.a1', '72.cr1.a1', '72.ct1.a1'], 'contains': ['288.a1.a1', '288.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7707, -1, 1867, -1, 8127, -1, 7472, -1], 'generators': [17, 4], 'label': '1152.156064.144.bp1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '144.bp1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983527
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '48.ck1.a1', '72.bb1.a1', '72.bw1.a1', '72.cc1.a1', '72.cj1.a1', '72.cm1.a1', '72.cr1.a1', '72.ct1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9002, -1, 2079, -1, 8343, -1, 7448, -1], 'generators': [2], 'label': '1152.156064.144.bq1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.bq1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983528
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '48.cl1.a1', '48.co1.a1', '72.be1.a1', '72.bw1.a1', '72.cd1.a1', '72.cj1.a1', '72.cn1.a1', '72.cq1.a1', '72.cs1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8853, -1, 2313, -1, 8281, -1, 7192, -1], 'generators': [18], 'label': '1152.156064.144.br1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '144.br1.a1', 'projective_image': '576.8353', '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: 60983529
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '72.y1.a1', '72.bx1.a1', '72.ck1.a1', '72.co1.a1', '72.co1.a2', '72.cu1.a1', '72.cu1.a2'], 'contains': ['288.j1.a1', '288.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7528, -1, 589, -1, 7080, -1, 9243, -1], 'generators': [1, 676], 'label': '1152.156064.144.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.bs1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983530
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1.a1', '72.ba1.a1', '72.bx1.a1', '72.ck1.a1', '72.cp1.a1', '72.cp1.a2', '72.cv1.a1', '72.cv1.a2'], 'contains': ['288.j1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7368, -1, 553, -1, 7051, -1, 9208, -1], 'generators': [17, 580], 'label': '1152.156064.144.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '144.bt1.a1', 'projective_image': '576.8353', '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': '8.3'}
  • id: 60983531
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1.a1', '72.bc1.a1', '72.by1.a1', '72.cl1.a1', '72.co1.a1', '72.co1.a2', '72.cv1.a1', '72.cv1.a2'], 'contains': ['288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7883, -1, 620, -1, 6709, -1, 9451, -1], 'generators': [98], 'label': '1152.156064.144.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.bu1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983532
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.a1', '72.bd1.a1', '72.by1.a1', '72.cl1.a1', '72.cp1.a1', '72.cp1.a2', '72.cu1.a1', '72.cu1.a2'], 'contains': ['288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7945, -1, 775, -1, 6681, -1, 9321, -1], 'generators': [114], 'label': '1152.156064.144.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '144.bv1.a1', 'projective_image': '576.8353', '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: 60983533
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '72.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.b1.a1', '24.c1.a1', '24.h1.a1', '24.i1.a1', '24.r1.a1', '24.s1.a1', '36.bi1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5962, 4523, 3737, 4268, 4405, 5863, 5423, 3473], 'generators': [4, 384, 8, 48, 96, 576], 'label': '1152.156064.12.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', '24.b1.a1', '24.c1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '576.8353', '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': '72.46'}
  • id: 60983534
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1.a1', '48.cm1.a1', '72.bi1.a1', '72.bv1.a1', '72.ck1.a1'], 'contains': ['288.k1.a1', '288.m1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6565, -1, 2293, -1, 6542, -1, 7262, -1], 'generators': [1, 60], 'label': '1152.156064.144.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '144.bw1.a1', 'projective_image': '576.8353', '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': '4.2'}
  • id: 60983535
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1.a1', '72.bi1.a1', '72.bx1.a1', '72.ci1.a1'], 'contains': ['288.l1.a1', '288.m1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6809, -1, 1810, -1, 7108, -1, 7566, -1], 'generators': [1, 732], 'label': '1152.156064.144.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '144.bx1.a1', 'projective_image': '576.8353', '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: 60983536
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1.a1', '72.bl1.a1', '72.cw1.a1'], 'contains': ['288.o1.a1', '288.p1.a1', '288.r1.b1', '288.v1.a1', '288.z1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1066, -1, 8130, -1, 1720, -1, 1275, -1], 'generators': [584, 48, 96], 'label': '1152.156064.144.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.by1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983537
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1.b1', '72.bl1.a1', '72.cw1.b1'], 'contains': ['288.o1.b1', '288.p1.a1', '288.r1.a1', '288.v1.b1', '288.z1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1066, -1, 8643, -1, 1720, -1, 1124, -1], 'generators': [584, 624, 96], 'label': '1152.156064.144.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.by1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983538
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cq1.a1', '72.b1.a1', '72.cw1.a1', '72.cx1.a1'], 'contains': ['288.o1.a1', '288.q1.a1', '288.t1.a1', '288.w1.a1', '288.x1.a1', '288.bf1.a1', '288.bg1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [849, -1, 8776, -1, 1570, -1, 930, -1], 'generators': [3, 48, 96], 'label': '1152.156064.144.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bz1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983539
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cq1.b1', '72.b1.a1', '72.cw1.b1', '72.cx1.b1'], 'contains': ['288.o1.b1', '288.q1.a1', '288.t1.a1', '288.w1.b1', '288.x1.b1', '288.bf1.b1', '288.bg1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [849, -1, 9182, -1, 1570, -1, 958, -1], 'generators': [3, 56, 96], 'label': '1152.156064.144.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.bz1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983540
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cr1.a1', '72.c1.a1', '72.cw1.a1', '72.cx1.a1'], 'contains': ['288.o1.a1', '288.s1.a1', '288.u1.a1', '288.x1.a1', '288.bh1.a1', '288.bh1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [809, -1, 8263, -1, 1441, -1, 821, -1], 'generators': [579, 48, 96], 'label': '1152.156064.144.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ca1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983541
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cr1.b1', '72.c1.a1', '72.cw1.b1', '72.cx1.b1'], 'contains': ['288.o1.b1', '288.s1.a1', '288.u1.a1', '288.x1.b1', '288.bh1.b1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [809, -1, 9160, -1, 1441, -1, 876, -1], 'generators': [579, 56, 96], 'label': '1152.156064.144.ca1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ca1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983542
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cs1.a1', '72.bm1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.p1.a1', '288.q1.a1', '288.s1.a1', '288.y1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1279, -1, 8819, -1, 1688, -1, 1151, -1], 'generators': [3, 584, 96], 'label': '1152.156064.144.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '144.cb1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983543
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ct1.a1', '72.bn1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.p1.a1', '288.t1.a1', '288.u1.a1', '288.bb1.a1', '288.bc1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1305, -1, 8688, -1, 1602, -1, 1178, -1], 'generators': [51, 584, 96], 'label': '1152.156064.144.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cc1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983544
    {'ambient': '1152.156064', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.p1.a1', '6.q1.a1'], 'contains': ['24.b1.a1', '24.o1.a1', '24.p1.a1', '24.x1.a1', '24.bq1.a1', '36.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4280, 703, 5804, 8531, 5046, 9241, 4938, 8645], 'generators': [3, 8, 384, 4, 96, 576], 'label': '1152.156064.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '576.8353', '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': '48.43'}
  • id: 60983545
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cu1.a1', '72.h1.a1', '72.cw1.b1', '72.cx1.a1'], 'contains': ['288.q1.a1', '288.r1.a1', '288.u1.a1', '288.bf1.a1', '288.bh1.a1', '288.bh1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [900, -1, 8841, -1, 1380, -1, 767, -1], 'generators': [3, 624, 96], 'label': '1152.156064.144.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cd1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983546
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cu1.b1', '72.h1.a1', '72.cw1.a1', '72.cx1.b1'], 'contains': ['288.q1.a1', '288.r1.b1', '288.u1.a1', '288.bf1.b1', '288.bh1.b1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [900, -1, 9226, -1, 1380, -1, 849, -1], 'generators': [3, 632, 96], 'label': '1152.156064.144.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cd1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983547
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cv1.a1', '72.m1.a1', '72.cw1.b1', '72.cx1.a1'], 'contains': ['288.r1.a1', '288.s1.a1', '288.t1.a1', '288.bg1.a1', '288.bh1.a1', '288.bh1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [990, -1, 9116, -1, 1538, -1, 794, -1], 'generators': [579, 624, 96], 'label': '1152.156064.144.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ce1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983548
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cv1.b1', '72.m1.a1', '72.cw1.a1', '72.cx1.b1'], 'contains': ['288.r1.b1', '288.s1.a1', '288.t1.a1', '288.bg1.b1', '288.bh1.b1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [990, -1, 9138, -1, 1538, -1, 903, -1], 'generators': [579, 632, 96], 'label': '1152.156064.144.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ce1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983549
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.cw1.a1', '72.bl1.a1', '72.cx1.a1'], 'contains': ['288.b1.a1', '288.o1.a1', '288.r1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [417, -1, 9428, -1, 891, -1, 639, -1], 'generators': [48, 96, 576], 'label': '1152.156064.144.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.cf1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983550
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.cw1.b1', '72.bl1.a1', '72.cx1.b1'], 'contains': ['288.b1.a1', '288.o1.b1', '288.r1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [417, -1, 9475, -1, 891, -1, 694, -1], 'generators': [56, 96, 576], 'label': '1152.156064.144.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.cf1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983551
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cx1.a1', '48.cy1.a1', '48.cz1.a1', '72.bm1.a1', '72.cx1.a1', '72.cx1.b1'], 'contains': ['288.b1.a1', '288.q1.a1', '288.s1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [378, -1, 9641, -1, 859, -1, 612, -1], 'generators': [3, 96, 576], 'label': '1152.156064.144.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '144.cg1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 60983552
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.da1.a1', '48.db1.a1', '72.bn1.a1', '72.cx1.a1', '72.cx1.b1'], 'contains': ['288.b1.a1', '288.t1.a1', '288.u1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [597, -1, 9453, -1, 827, -1, 667, -1], 'generators': [51, 96, 576], 'label': '1152.156064.144.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '144.ch1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 60983553
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dc1.a1', '72.b1.a1', '72.cw1.a1'], 'contains': ['288.v1.a1', '288.w1.a1', '288.x1.a1', '288.y1.a1', '288.bb1.a1', '288.bf1.b1', '288.bg1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1743, -1, 8590, -1, 1975, -1, 1556, -1], 'generators': [3, 104, 48], 'label': '1152.156064.144.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ci1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983554
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dc1.b1', '72.b1.a1', '72.cw1.b1'], 'contains': ['288.v1.b1', '288.w1.b1', '288.x1.b1', '288.y1.a1', '288.bb1.a1', '288.bf1.a1', '288.bg1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1743, -1, 8215, -1, 1975, -1, 1529, -1], 'generators': [3, 104, 144], 'label': '1152.156064.144.ci1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.ci1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983555
    {'ambient': '1152.156064', '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': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.k1.a1', '6.r1.a1'], 'contains': ['24.d1.a1', '24.br1.a1', '36.a1.a1', '48.bh1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4166, 3064, 6405, 9583, 1945, 7008, 2938, 6556], 'generators': [3, 576, 96, 4, 32, 8], 'label': '1152.156064.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.b1.a1', '6.b1.a1'], 'normal_contains': ['24.d1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 60983556
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dd1.a1', '72.c1.a1', '72.cw1.a1'], 'contains': ['288.v1.a1', '288.x1.a1', '288.ba1.a1', '288.bc1.a1', '288.bh1.b1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2139, -1, 7192, -1, 2122, -1, 1611, -1], 'generators': [579, 104, 48], 'label': '1152.156064.144.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cj1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983557
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dd1.b1', '72.c1.a1', '72.cw1.b1'], 'contains': ['288.v1.b1', '288.x1.b1', '288.ba1.a1', '288.bc1.a1', '288.bh1.a1', '288.bh1.a2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2139, -1, 7598, -1, 2122, -1, 1583, -1], 'generators': [579, 104, 144], 'label': '1152.156064.144.cj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cj1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983558
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.de1.a1', '72.f1.a1'], 'contains': ['288.v1.a1', '288.bd1.a1', '288.be1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4645, -1, 4390, -1, 4446, -1, 5657, -1], 'generators': [97, 48], 'label': '1152.156064.144.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '144.ck1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983559
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.de1.b1', '72.f1.a1'], 'contains': ['288.v1.b1', '288.bd1.a1', '288.be1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4645, -1, 4352, -1, 4446, -1, 5581, -1], 'generators': [97, 720], 'label': '1152.156064.144.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '144.ck1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983560
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.df1.a1', '72.h1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.y1.a1', '288.z1.a1', '288.bc1.a1', '288.bf1.a1', '288.bf1.b1', '288.bh1.a2', '288.bh1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1919, -1, 8295, -1, 2008, -1, 1419, -1], 'generators': [3, 104, 624], 'label': '1152.156064.144.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cl1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983561
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.df1.a2', '72.h1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.y1.a1', '288.z1.a1', '288.bc1.a1', '288.bf1.a1', '288.bf1.b1', '288.bh1.a1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1919, -1, 8241, -1, 2008, -1, 1447, -1], 'generators': [3, 104, 720], 'label': '1152.156064.144.cl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cl1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983562
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dg1.a1', '72.m1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.z1.a1', '288.ba1.a1', '288.bb1.a1', '288.bg1.a1', '288.bg1.b1', '288.bh1.a2', '288.bh1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2100, -1, 8175, -1, 2154, -1, 1474, -1], 'generators': [579, 104, 720], 'label': '1152.156064.144.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cm1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983563
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dg1.a2', '72.m1.a1', '72.cw1.a1', '72.cw1.b1'], 'contains': ['288.z1.a1', '288.ba1.a1', '288.bb1.a1', '288.bg1.a1', '288.bg1.b1', '288.bh1.a1', '288.bh1.b2'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2100, -1, 8153, -1, 2154, -1, 1501, -1], 'generators': [579, 104, 624], 'label': '1152.156064.144.cm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '144.cm1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983564
    {'ambient': '1152.156064', 'aut_centralizer_order': 2304, 'aut_label': '192.a1', 'aut_quo_index': 8, '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.b1.a1', '96.c1.a1', '96.f1.a1', '96.h1.a1', '96.k1.a1', '96.l1.a1', '96.n1.a1', '96.o1.a1', '96.p1.a1', '96.q1.a1', '96.r1.a1', '96.s1.a1'], 'contains': ['384.a1.a1', '576.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2971, 5872, 5177, 3682, 4004, 4781, 3640, 4212], 'generators': [8, 384], 'label': '1152.156064.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normal_contains': ['384.a1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.195', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983565
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.b1.a1', 'complements': ['6.b1.a1', '6.u1.a1', '6.t1.a1', '6.r1.a1', '6.s1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.a1.a1', '96.z1.a1', '96.bi1.a1', '96.bj1.a1', '96.bk1.a1'], 'contains': ['384.a1.a1', '576.c1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1095, 7272, 6704, 2322, 1764, 3978, 1862, 3572], 'generators': [48, 384], 'label': '1152.156064.192.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': ['48.f1.a1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.973', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983566
    {'ambient': '1152.156064', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.v1.a1', '6.w1.a1'], 'contains': ['24.b1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bu1.a1', '36.bl1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5136, 2006, 4158, 5985, 4968, 8009, 4872, 7493], 'generators': [51, 384, 8, 4, 96, 576], 'label': '1152.156064.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.153'}
  • id: 60983567
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.b1.a1', 'complements': ['6.b1.a1', '6.u1.a1', '6.t1.a1', '6.r1.a1', '6.s1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '96.a1.a1', '96.z1.b1', '96.bi1.b1', '96.bj1.b1', '96.bk1.b1'], 'contains': ['384.a1.a1', '576.c1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1095, 7272, 7177, 2986, 1764, 3978, 1886, 3153], 'generators': [56, 384], 'label': '1152.156064.192.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.b1.b1', 'normal_contained_in': ['48.f1.b1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.b1', 'projective_image': '1152.156064', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.973', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983568
    {'ambient': '1152.156064', 'aut_centralizer_order': 576, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '64.a1.a1', '96.g1.a1', '96.i1.a1', '96.m1.a1', '96.t1.a1', '96.u1.a1', '96.v1.a1', '96.w1.a1'], 'contains': ['384.b1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1406, -1, 7761, -1, 1094, -1, 2248, -1], 'generators': [8, 32], 'label': '1152.156064.192.c1.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.c1.a1', 'projective_image': '576.8353', '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: 60983569
    {'ambient': '1152.156064', 'aut_centralizer_order': 288, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '64.a1.a1', '96.j1.a1', '96.x1.a1', '96.y1.a1'], 'contains': ['384.c1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 7554, -1, 2287, -1, 2323, -1], 'generators': [8, 416], 'label': '1152.156064.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1.a1', 'old_label': '192.d1.a1', 'projective_image': '576.8353', '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: 60983570
    {'ambient': '1152.156064', '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.d1.a1', '96.f1.a1', '96.z1.a1', '96.z1.b1', '96.ba1.a1', '96.bb1.a1', '96.bc1.a1', '96.bc1.b1', '96.bd1.a1', '96.be1.a1', '96.bf1.a1'], 'contains': ['384.a1.a1', '576.b1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [680, -1, 8921, -1, 1411, -1, 1203, -1], 'generators': [96, 384], 'label': '1152.156064.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.e1.a1', 'projective_image': '1152.156064', '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: 60983571
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cw1.a1', '64.b1.a1', '96.g1.a1', '96.bh1.a1'], 'contains': ['384.b1.a1', '576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [136, -1, 8673, -1, 647, -1, 504, -1], 'generators': [48, 32], 'label': '1152.156064.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '192.f1.a1', 'projective_image': '1152.156064', '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: 60983572
    {'ambient': '1152.156064', 'aut_centralizer_order': 96, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cw1.b1', '64.b1.b1', '96.g1.a1', '96.bh1.b1'], 'contains': ['384.b1.a1', '576.c1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [136, -1, 8941, -1, 647, -1, 569, -1], 'generators': [56, 32], 'label': '1152.156064.192.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '192.f1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983573
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '192.g1', '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.f1.a1', '96.ba1.a1', '96.bi1.a1', '96.bi1.b1', '96.bl1.a1', '96.bm1.a1', '96.bn1.a1', '96.bo1.a1', '96.bp1.a1', '96.bq1.a1', '96.br1.a1'], 'contains': ['384.a1.a1', '576.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1966, -1, 6628, -1, 2167, -1, 2030, -1], 'generators': [104, 384], 'label': '1152.156064.192.g1.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.g1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983574
    {'ambient': '1152.156064', 'aut_centralizer_order': 576, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.h1.a1', '96.bb1.a1', '96.bj1.a1', '96.bj1.b1', '96.bl1.a1', '96.bs1.a1', '96.bs1.b1'], 'contains': ['384.a1.a1', '576.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1072, -1, 8435, -1, 1707, -1, 1742, -1], 'generators': [3, 384], 'label': '1152.156064.192.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '192.h1.a1', 'projective_image': '1152.156064', '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: 60983575
    {'ambient': '1152.156064', 'aut_centralizer_order': 144, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cy1.a1', '64.c1.a1', '96.i1.a1', '96.bh1.a1', '96.bh1.b1'], 'contains': ['384.b1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [46, -1, 9915, -1, 619, -1, 438, -1], 'generators': [3, 32], 'label': '1152.156064.192.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '192.i1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983576
    {'ambient': '1152.156064', 'aut_centralizer_order': 72, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cz1.a1', '64.c1.a1', '96.j1.a1'], 'contains': ['384.c1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [186, -1, 9742, -1, 752, -1, 414, -1], 'generators': [3, 416], 'label': '1152.156064.192.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.c1.a1', 'old_label': '192.j1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983577
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.bj1.a1', '96.bk1.a1', '96.bs1.a1', '96.bt1.a1', '96.bu1.a2', '96.bu1.a1', '96.bj1.b1', '96.bk1.b1', '96.bs1.b1', '96.bt1.b1', '96.bu1.b2', '96.bu1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.l1.a1', '6.t1.a1'], 'contains': ['24.d1.a1', '24.by1.a1', '36.bm1.a1', '48.ci1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4894, 5589, 5535, 6826, 1900, 4289, 3007, 5893], 'generators': [1, 576, 672, 4, 8, 32], 'label': '1152.156064.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1'], 'normal_contains': ['24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '576.8353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 60983578
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.z1.a1', '96.bc1.a1', '96.bi1.b1', '96.bm1.a1', '96.bs1.a1', '96.bt1.a1', '96.bu1.a1', '96.bu1.a2'], 'contains': ['384.a1.a1', '576.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1842, -1, 7008, -1, 1946, -1, 1718, -1], 'generators': [144, 384], 'label': '1152.156064.192.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.k1.a1', 'projective_image': '1152.156064', '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: 60983579
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.z1.b1', '96.bc1.b1', '96.bi1.a1', '96.bm1.a1', '96.bs1.b1', '96.bt1.b1', '96.bu1.b1', '96.bu1.b2'], 'contains': ['384.a1.a1', '576.f1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1842, -1, 7856, -1, 1946, -1, 1790, -1], 'generators': [152, 384], 'label': '1152.156064.192.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.k1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983580
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1.a1', '96.bb1.a1', '96.bd1.a1', '96.bk1.a1', '96.bk1.b1', '96.bl1.a1', '96.bn1.a1', '96.bt1.a1', '96.bt1.b1', '96.bu1.a1', '96.bu1.a2', '96.bu1.b1', '96.bu1.b2'], 'contains': ['384.a1.a1', '576.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1450, -1, 7431, -1, 1821, -1, 1814, -1], 'generators': [99, 384], 'label': '1152.156064.192.l1.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': '192.l1.a1', 'projective_image': '1152.156064', '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': '2.1'}
  • id: 60983582
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '24.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '96.n1.a1', '96.be1.a1', '96.bj1.a1', '96.bj1.b1', '96.bo1.a1', '96.bt1.a1', '96.bt1.b1'], 'contains': ['384.a1.a1', '576.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1296, -1, 7875, -1, 1736, -1, 1838, -1], 'generators': [51, 384], 'label': '1152.156064.192.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '192.n1.a1', 'projective_image': '1152.156064', '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: 60983583
    {'ambient': '1152.156064', '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.o1.a1', '96.be1.a1', '96.bf1.a1', '96.bk1.a1', '96.bk1.b1', '96.bo1.a1', '96.bp1.a1', '96.bs1.a1', '96.bs1.b1', '96.bu1.a1', '96.bu1.a2', '96.bu1.b1', '96.bu1.b2'], 'contains': ['384.a1.a1', '576.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1574, -1, 7390, -1, 1792, -1, 1766, -1], 'generators': [147, 384], 'label': '1152.156064.192.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '192.o1.a1', 'projective_image': '1152.156064', '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: 60983584
    {'ambient': '1152.156064', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.t1.a1', '96.x1.a1', '144.b1.a1', '144.i1.a1', '144.s1.a1', '144.bb1.a1', '144.bi1.a1', '144.bl1.a1', '144.bm1.a1', '144.bo1.a1', '144.bp1.a1', '144.bq1.a1', '144.br1.a1'], 'contains': ['576.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6374, 4254, 4027, 5974, 6820, 6398, 5695, 5969], 'generators': [4], 'label': '1152.156064.288.a1.a1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.b1.a1', '144.b1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '576.8353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983585
    {'ambient': '1152.156064', '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.d1.a1', '96.e1.a1', '96.bg1.a1', '144.a1.a1', '144.cf1.a1', '144.cf1.b1', '144.cg1.a1', '144.ch1.a1'], 'contains': ['576.b1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [486, 8410, 9444, 2001, 843, 3244, 667, 2705], 'generators': [96, 576], 'label': '1152.156064.288.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['96.d1.a1', '96.e1.a1', '144.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '6.1', 'quotient_action_kernel': '48.38', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60983586
    {'ambient': '1152.156064', '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.f1.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.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3554, -1, 5786, -1, 3691, -1, 3665, -1], 'generators': [8, 96], 'label': '1152.156064.288.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': '576.8353', '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: 60983587
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.g1.a1', '144.c1.a1', '144.q1.a1', '144.r1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1'], 'contains': ['576.a1.a1', '576.c1.a1', '576.c1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3192, -1, 5821, -1, 4486, -1, 3614, -1], 'generators': [8, 48], 'label': '1152.156064.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.d1.a1', 'projective_image': '576.8353', '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': '1.1'}
  • id: 60983588
    {'ambient': '1152.156064', '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.c1.a1', 'complements': ['96.bj1.a1', '96.bk1.a1', '96.bs1.a1', '96.bt1.a1', '96.bu1.a2', '96.bu1.a1', '96.bj1.b1', '96.bk1.b1', '96.bs1.b1', '96.bt1.b1', '96.bu1.b2', '96.bu1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.m1.a1', '6.u1.a1'], 'contains': ['24.d1.a1', '36.bo1.a1', '48.ck1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7408, 6444, 4006, 7382, 2519, 4862, 4456, 5358], 'generators': [2, 576, 672, 4, 8, 32], 'label': '1152.156064.12.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.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '576.8353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60983589
    {'ambient': '1152.156064', 'aut_centralizer_order': 1152, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.i1.a1', '96.j1.a1', '144.b1.a1', '144.d1.a1', '144.q1.a1', '144.v1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1'], 'contains': ['576.a1.a1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2374, -1, 7694, -1, 3659, -1, 2908, -1], 'generators': [3, 8], 'label': '1152.156064.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '288.e1.a1', 'projective_image': '576.8353', '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: 60983590
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '144.c1.a1', '144.e1.a1', '144.v1.a1', '144.z1.a1', '144.ba1.a1', '144.ba1.a2', '144.bb1.a1', '144.bc1.a1', '144.bd1.a1', '144.be1.a1'], 'contains': ['576.a1.a1', '576.f1.a1', '576.f1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3411, -1, 6734, -1, 3941, -1, 3531, -1], 'generators': [8, 144], 'label': '1152.156064.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.f1.a1', 'projective_image': '576.8353', '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': '1.1'}
  • id: 60983591
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1.a1', '144.d1.a1', '144.f1.a1', '144.r1.a1', '144.w1.a1', '144.z1.a1', '144.ba1.a1', '144.ba1.a2', '144.bf1.a1', '144.bg1.a1', '144.bh1.a1', '144.bh1.a2', '144.bi1.a1', '144.bj1.a1', '144.bj1.a2'], 'contains': ['576.a1.a1', '576.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3292, -1, 6168, -1, 3974, -1, 3587, -1], 'generators': [99, 8], 'label': '1152.156064.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '288.g1.a1', 'projective_image': '576.8353', '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: 60983592
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '288.h1', '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.m1.a1', '96.n1.a1', '144.g1.a1', '144.q1.a1', '144.x1.a1', '144.z1.a1', '144.bf1.a1', '144.bk1.a1', '144.bl1.a1'], 'contains': ['576.a1.a1', '576.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3027, -1, 7241, -1, 3795, -1, 3453, -1], 'generators': [51, 8], 'label': '1152.156064.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '288.h1.a1', 'projective_image': '576.8353', '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: 60983593
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '288.i1', '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.o1.a1', '144.g1.a1', '144.h1.a1', '144.r1.a1', '144.v1.a1', '144.y1.a1', '144.ba1.a1', '144.ba1.a2', '144.bg1.a1', '144.bh1.a1', '144.bh1.a2', '144.bk1.a1', '144.bm1.a1', '144.bn1.a1', '144.bn1.a2'], 'contains': ['576.a1.a1', '576.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3319, -1, 5854, -1, 3907, -1, 3504, -1], 'generators': [147, 8], 'label': '1152.156064.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '288.i1.a1', 'projective_image': '576.8353', '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: 60983594
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '144.i1.a1', '144.j1.a1', '144.t1.a1', '144.w1.a1', '144.bc1.a1', '144.bd1.a1', '144.bj1.a1', '144.bj1.a2', '144.bk1.a1', '144.bn1.a1', '144.bn1.a2', '144.bs1.a1', '144.bt1.a1', '144.bu1.a1', '144.bv1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5474, -1, 3523, -1, 5885, -1, 5777, -1], 'generators': [100], 'label': '1152.156064.288.j1.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.j1.a1', 'projective_image': '576.8353', '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: 60983595
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.u1.a1', '144.k1.a1', '144.s1.a1', '144.x1.a1', '144.bc1.a1', '144.bg1.a1', '144.bw1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4811, -1, 4121, -1, 5429, -1, 4774, -1], 'generators': [60], 'label': '1152.156064.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.k1.a1', 'projective_image': '576.8353', '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: 60983596
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.a1', '144.k1.a1', '144.l1.a1', '144.t1.a1', '144.y1.a1', '144.bb1.a1', '144.bd1.a1', '144.bf1.a1', '144.bh1.a1', '144.bh1.a2', '144.bx1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4773, -1, 4204, -1, 4086, -1, 4717, -1], 'generators': [156], 'label': '1152.156064.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.l1.a1', 'projective_image': '576.8353', '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: 60983597
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '96.v1.a1', '144.n1.a1', '144.u1.a1', '144.be1.a1', '144.bo1.a1', '144.bs1.a1', '144.bw1.a1', '144.bx1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6318, -1, 2474, -1, 6673, -1, 7256, -1], 'generators': [1], 'label': '1152.156064.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '288.m1.a1', 'projective_image': '576.8353', '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': '2.1'}
  • id: 60983598
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1.a1', '96.w1.a1', '96.y1.a1', '144.p1.a1', '144.u1.a1', '144.be1.a1', '144.bp1.a1', '144.bt1.a1', '144.bw1.a1', '144.bx1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6162, -1, 2345, -1, 6542, -1, 7227, -1], 'generators': [17], 'label': '1152.156064.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '288.n1.a1', 'projective_image': '576.8353', '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: 60983599
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.i1.a1', '24.n1.a1', '24.o1.a1', '24.v1.a1', '24.y1.a1', '24.cf1.a1', '24.ch1.a1', '24.ch1.a2', '24.cn1.a1', '24.cn1.a2', '24.cu1.a1', '24.cu1.a2', '36.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3037, -1, 5883, -1, 3721, -1, 3861, -1], 'generators': [3, 384, 8, 580, 48, 96], 'label': '1152.156064.12.g1.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': '12.g1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983600
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.z1.a1', '144.c1.a1', '144.by1.a1', '144.bz1.a1', '144.ca1.a1', '144.cf1.a1'], 'contains': ['576.b1.a1', '576.c1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [841, -1, 7922, -1, 1613, -1, 1150, -1], 'generators': [48, 96], 'label': '1152.156064.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.o1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983601
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.z1.b1', '144.c1.a1', '144.by1.b1', '144.bz1.b1', '144.ca1.b1', '144.cf1.b1'], 'contains': ['576.b1.a1', '576.c1.b1', '576.f1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [841, -1, 8953, -1, 1613, -1, 1177, -1], 'generators': [56, 96], 'label': '1152.156064.288.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.o1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983602
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '288.p1', '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.ba1.a1', '144.a1.a1', '144.by1.a1', '144.by1.b1', '144.cb1.a1', '144.cc1.a1'], 'contains': ['576.b1.a1', '576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1176, -1, 8313, -1, 1645, -1, 1228, -1], 'generators': [584, 96], 'label': '1152.156064.288.p1.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.p1.a1', 'projective_image': '1152.156064', '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: 60983603
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '144.d1.a1', '144.bz1.a1', '144.bz1.b1', '144.cb1.a1', '144.cd1.a1', '144.cd1.b1', '144.cg1.a1'], 'contains': ['576.b1.a1', '576.e1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [754, -1, 8976, -1, 1516, -1, 1068, -1], 'generators': [3, 96], 'label': '1152.156064.288.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.q1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983604
    {'ambient': '1152.156064', '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': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1.a1', '144.e1.a1', '144.by1.b1', '144.cd1.a1', '144.ce1.a1', '144.cf1.a1'], 'contains': ['576.b1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1042, -1, 8841, -1, 1580, -1, 986, -1], 'generators': [624, 96], 'label': '1152.156064.288.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.r1.a1', 'projective_image': '1152.156064', '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: 60983605
    {'ambient': '1152.156064', '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': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1.b1', '144.e1.a1', '144.by1.a1', '144.cd1.b1', '144.ce1.b1', '144.cf1.b1'], 'contains': ['576.b1.a1', '576.f1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1042, -1, 9351, -1, 1580, -1, 1095, -1], 'generators': [632, 96], 'label': '1152.156064.288.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.r1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983606
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bd1.a1', '144.f1.a1', '144.ca1.a1', '144.ca1.b1', '144.cb1.a1', '144.ce1.a1', '144.ce1.b1', '144.cg1.a1'], 'contains': ['576.b1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [870, -1, 8931, -1, 1484, -1, 1040, -1], 'generators': [579, 96], 'label': '1152.156064.288.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.s1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983607
    {'ambient': '1152.156064', '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.g1.a1', '144.bz1.a1', '144.bz1.b1', '144.cc1.a1', '144.ce1.a1', '144.ce1.b1', '144.ch1.a1'], 'contains': ['576.b1.a1', '576.h1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1015, -1, 8887, -1, 1548, -1, 1122, -1], 'generators': [51, 96], 'label': '1152.156064.288.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.t1.a1', 'projective_image': '1152.156064', '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: 60983608
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bf1.a1', '144.h1.a1', '144.ca1.a1', '144.ca1.b1', '144.cc1.a1', '144.cd1.a1', '144.cd1.b1', '144.ch1.a1'], 'contains': ['576.b1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [916, -1, 8909, -1, 1446, -1, 1013, -1], 'generators': [627, 96], 'label': '1152.156064.288.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.u1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983609
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bi1.a1', '144.c1.a1', '144.by1.a1', '144.ci1.a1', '144.cj1.a1', '144.ck1.a1'], 'contains': ['576.c1.a1', '576.d1.a1', '576.f1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2113, -1, 7162, -1, 2198, -1, 1939, -1], 'generators': [104, 48], 'label': '1152.156064.288.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.v1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983610
    {'ambient': '1152.156064', '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.c1.a1', '576.f1.a1', '576.c1.b1', '576.f1.b1', '576.e1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '6.t1.a1', '6.v1.a1', '8.m1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5130, 4149, 4708, 4250, 2294, 4065, 3421, 5323], 'generators': [1, 32, 384, 18, 8, 576, 672, 12], 'label': '1152.156064.2.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.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '576.8353', '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': '576.8353'}
  • id: 60983611
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.h1', '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.d1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.h1.a1', '24.m1.a1', '24.p1.a1', '24.z1.a1', '24.cf1.a1', '24.cg1.a1', '24.cm1.a1', '24.co1.a1', '24.cv1.a1', '36.c1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4460, -1, 6226, -1, 6012, -1, 4553, -1], 'generators': [3, 384, 8, 4, 48, 96], 'label': '1152.156064.12.h1.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.h1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983612
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bi1.b1', '144.c1.a1', '144.by1.b1', '144.ci1.b1', '144.cj1.b1', '144.ck1.b1'], 'contains': ['576.c1.b1', '576.d1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2113, -1, 7198, -1, 2198, -1, 1912, -1], 'generators': [104, 144], 'label': '1152.156064.288.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.v1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983613
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1.a1', '96.bj1.a1', '144.q1.a1', '144.bz1.a1', '144.ci1.a1'], 'contains': ['576.c1.a1', '576.e1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [988, -1, 8516, -1, 1677, -1, 1474, -1], 'generators': [3, 48], 'label': '1152.156064.288.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '288.w1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983614
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1.b1', '96.bj1.b1', '144.q1.a1', '144.bz1.b1', '144.ci1.b1'], 'contains': ['576.c1.b1', '576.e1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [988, -1, 8539, -1, 1677, -1, 1529, -1], 'generators': [3, 56], 'label': '1152.156064.288.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '288.w1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983615
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1.a1', '144.r1.a1', '144.bz1.a1', '144.ca1.a1', '144.ci1.a1', '144.cj1.a1'], 'contains': ['576.c1.a1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1561, -1, 7896, -1, 1883, -1, 1583, -1], 'generators': [99, 48], 'label': '1152.156064.288.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.x1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983616
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1.b1', '144.r1.a1', '144.bz1.b1', '144.ca1.b1', '144.ci1.b1', '144.cj1.b1'], 'contains': ['576.c1.b1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1561, -1, 8026, -1, 1883, -1, 1611, -1], 'generators': [99, 56], 'label': '1152.156064.288.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.x1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983617
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bl1.a1', '144.d1.a1', '144.cb1.a1', '144.ci1.a1', '144.ci1.b1', '144.cl1.a1', '144.cl1.a2'], 'contains': ['576.d1.a1', '576.e1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1743, -1, 8280, -1, 2008, -1, 1556, -1], 'generators': [3, 104], 'label': '1152.156064.288.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.y1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983618
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bm1.a1', '144.e1.a1', '144.by1.a1', '144.by1.b1', '144.cl1.a1', '144.cl1.a2', '144.cm1.a1', '144.cm1.a2'], 'contains': ['576.d1.a1', '576.f1.a1', '576.f1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2139, -1, 7958, -1, 2137, -1, 1419, -1], 'generators': [104, 624], 'label': '1152.156064.288.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '288.z1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983619
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1.a1', '144.f1.a1', '144.cb1.a1', '144.cj1.a1', '144.cj1.b1', '144.cm1.a1', '144.cm1.a2'], 'contains': ['576.d1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2047, -1, 7661, -1, 2105, -1, 1693, -1], 'generators': [579, 104], 'label': '1152.156064.288.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '288.ba1.a1', 'projective_image': '1152.156064', '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': '1.1'}
  • id: 60983620
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '288.bb1', '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.bo1.a1', '144.g1.a1', '144.cc1.a1', '144.ci1.a1', '144.ci1.b1', '144.cm1.a1', '144.cm1.a2'], 'contains': ['576.d1.a1', '576.h1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1810, -1, 8073, -1, 2040, -1, 1638, -1], 'generators': [51, 104], 'label': '1152.156064.288.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bb1.a1', 'projective_image': '1152.156064', '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: 60983621
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bp1.a1', '144.h1.a1', '144.cc1.a1', '144.cj1.a1', '144.cj1.b1', '144.cl1.a1', '144.cl1.a2'], 'contains': ['576.d1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2074, -1, 7628, -1, 2073, -1, 1665, -1], 'generators': [627, 104], 'label': '1152.156064.288.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bc1.a1', 'projective_image': '1152.156064', '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: 60983622
    {'ambient': '1152.156064', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.w1.a1', '24.x1.a1', '24.ba1.a1', '24.cg1.a1', '24.ch1.a1', '24.ch1.a2', '24.cw1.a1', '24.cx1.a1', '24.cx1.a2', '36.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6133, -1, 4424, -1, 5628, -1, 5166, -1], 'generators': [579, 384, 8, 4, 48, 96], 'label': '1152.156064.12.i1.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.i1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983623
    {'ambient': '1152.156064', 'aut_centralizer_order': 192, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bq1.a1', '144.m1.a1', '144.ck1.a1', '144.ck1.b1'], 'contains': ['576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4599, -1, 4412, -1, 4424, -1, 5581, -1], 'generators': [97], 'label': '1152.156064.288.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '288.bd1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983624
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.br1.a1', '144.o1.a1', '144.ck1.a1', '144.ck1.b1'], 'contains': ['576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3511, -1, 4371, -1, 4392, -1, 5620, -1], 'generators': [113], 'label': '1152.156064.288.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '288.be1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983625
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bs1.a1', '144.v1.a1', '144.bz1.a1', '144.cd1.a1', '144.ci1.b1', '144.cl1.a1', '144.cl1.a2'], 'contains': ['576.e1.a1', '576.f1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1695, -1, 8258, -1, 1851, -1, 1256, -1], 'generators': [3, 144], 'label': '1152.156064.288.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bf1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983626
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bs1.b1', '144.v1.a1', '144.bz1.b1', '144.cd1.b1', '144.ci1.a1', '144.cl1.a1', '144.cl1.a2'], 'contains': ['576.e1.a1', '576.f1.b1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1695, -1, 8447, -1, 1851, -1, 1337, -1], 'generators': [3, 152], 'label': '1152.156064.288.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bf1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983627
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bt1.a1', '144.z1.a1', '144.bz1.a1', '144.ce1.a1', '144.ci1.b1', '144.cm1.a1', '144.cm1.a2'], 'contains': ['576.f1.a1', '576.g1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1599, -1, 8224, -1, 1976, -1, 1447, -1], 'generators': [99, 144], 'label': '1152.156064.288.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bg1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983628
    {'ambient': '1152.156064', 'aut_centralizer_order': 64, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bt1.b1', '144.z1.a1', '144.bz1.b1', '144.ce1.b1', '144.ci1.a1', '144.cm1.a1', '144.cm1.a2'], 'contains': ['576.f1.b1', '576.g1.a1', '576.h1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1599, -1, 8401, -1, 1976, -1, 1501, -1], 'generators': [99, 152], 'label': '1152.156064.288.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bg1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983629
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bu1.a1', '144.ba1.a1', '144.ca1.a1', '144.cd1.a1', '144.ce1.a1', '144.cj1.b1', '144.cl1.a2', '144.cm1.a2'], 'contains': ['576.f1.a1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1783, -1, 8095, -1, 1915, -1, 1310, -1], 'generators': [579, 144], 'label': '1152.156064.288.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bh1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983630
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bu1.a2', '144.ba1.a2', '144.ca1.a1', '144.cd1.a1', '144.ce1.a1', '144.cj1.b1', '144.cl1.a1', '144.cm1.a1'], 'contains': ['576.f1.a1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1783, -1, 8130, -1, 1915, -1, 1283, -1], 'generators': [675, 144], 'label': '1152.156064.288.bh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bh1.a2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983631
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bu1.b1', '144.ba1.a1', '144.ca1.b1', '144.cd1.b1', '144.ce1.b1', '144.cj1.a1', '144.cl1.a1', '144.cm1.a1'], 'contains': ['576.f1.b1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1783, -1, 8379, -1, 1915, -1, 1365, -1], 'generators': [579, 152], 'label': '1152.156064.288.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bh1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983632
    {'ambient': '1152.156064', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bu1.b2', '144.ba1.a2', '144.ca1.b1', '144.cd1.b1', '144.ce1.b1', '144.cj1.a1', '144.cl1.a2', '144.cm1.a2'], 'contains': ['576.f1.b1', '576.g1.a1', '576.i1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1783, -1, 8356, -1, 1915, -1, 1392, -1], 'generators': [675, 152], 'label': '1152.156064.288.bh1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '288.bh1.b2', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983633
    {'ambient': '1152.156064', '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.n1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.bb1.a1', '24.bd1.a1', '24.bl1.a1', '36.e1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6506, -1, 3386, -1, 5271, -1, 5929, -1], 'generators': [577, 384, 672, 4, 48, 680], 'label': '1152.156064.12.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': '576.8353', '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: 60983634
    {'ambient': '1152.156064', 'aut_centralizer_order': 2304, 'aut_label': '384.a1', 'aut_quo_index': 4, '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.b1.a1', '192.b1.b1', '192.e1.a1', '192.g1.a1', '192.h1.a1', '192.k1.a1', '192.k1.b1', '192.l1.a1', '192.n1.a1', '192.o1.a1'], 'contains': ['1152.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1314, 7272, 7431, 2703, 1792, 3978, 1778, 3310], 'generators': [384], 'label': '1152.156064.384.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.d1.a1', '192.a1.a1', '192.b1.b1', '192.b1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '1152.156064', 'quotient_action_image': '2.1', 'quotient_action_kernel': '192.973', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60983635
    {'ambient': '1152.156064', '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.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '128.a1.a1', '192.c1.a1', '192.f1.a1', '192.f1.b1', '192.i1.a1', '192.m1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [43, -1, 9721, -1, 647, -1, 529, -1], 'generators': [32], 'label': '1152.156064.384.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '384.b1.a1', 'projective_image': '1152.156064', '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: 60983636
    {'ambient': '1152.156064', '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.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1.a1', '128.a1.a1', '192.d1.a1', '192.j1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [167, -1, 9702, -1, 774, -1, 505, -1], 'generators': [416], 'label': '1152.156064.384.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1.a1', 'old_label': '384.c1.a1', 'projective_image': '1152.156064', '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: 60983637
    {'ambient': '1152.156064', 'aut_centralizer_order': 4608, 'aut_label': '576.a1', 'aut_quo_index': 2, '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.c1.a1', '192.d1.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', '288.m1.a1', '288.n1.a1'], 'contains': ['1152.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3319, 6523, 5823, 3483, 3974, 4607, 3614, 4049], 'generators': [8], 'label': '1152.156064.576.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': '576.8353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '576.8353', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983638
    {'ambient': '1152.156064', '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.e1.a1', '288.b1.a1', '288.c1.a1', '288.o1.a1', '288.o1.b1', '288.p1.a1', '288.q1.a1', '288.r1.a1', '288.r1.b1', '288.s1.a1', '288.t1.a1', '288.u1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [916, -1, 8887, -1, 1548, -1, 1122, -1], 'generators': [96], 'label': '1152.156064.576.b1.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.b1.a1', 'projective_image': '1152.156064', '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: 60983639
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.f1.a1', '288.d1.a1', '288.o1.a1', '288.v1.a1', '288.w1.a1', '288.x1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1199, -1, 7747, -1, 1764, -1, 1516, -1], 'generators': [48], 'label': '1152.156064.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '576.c1.a1', 'projective_image': '1152.156064', '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: 60983640
    {'ambient': '1152.156064', 'aut_centralizer_order': 768, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.b1', '192.f1.b1', '288.d1.a1', '288.o1.b1', '288.v1.b1', '288.w1.b1', '288.x1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1199, -1, 8043, -1, 1764, -1, 1541, -1], 'generators': [56], 'label': '1152.156064.576.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '576.c1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983641
    {'ambient': '1152.156064', 'aut_centralizer_order': 1536, 'aut_label': '576.d1', '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.g1.a1', '288.c1.a1', '288.p1.a1', '288.v1.a1', '288.v1.b1', '288.y1.a1', '288.z1.a1', '288.ba1.a1', '288.bb1.a1', '288.bc1.a1', '288.bd1.a1', '288.be1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1911, -1, 7628, -1, 2121, -1, 1802, -1], 'generators': [104], 'label': '1152.156064.576.d1.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.d1.a1', 'projective_image': '1152.156064', '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: 60983642
    {'ambient': '1152.156064', 'aut_centralizer_order': 1152, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.h1.a1', '192.i1.a1', '192.j1.a1', '288.e1.a1', '288.q1.a1', '288.w1.a1', '288.w1.b1', '288.y1.a1', '288.bf1.a1', '288.bf1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1072, -1, 8468, -1, 1707, -1, 1349, -1], 'generators': [3], 'label': '1152.156064.576.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '576.e1.a1', 'projective_image': '1152.156064', '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: 60983643
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.k1.a1', '288.f1.a1', '288.o1.a1', '288.r1.a1', '288.v1.b1', '288.z1.a1', '288.bf1.a1', '288.bg1.a1', '288.bh1.a1', '288.bh1.a2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1700, -1, 7990, -1, 1930, -1, 1373, -1], 'generators': [144], 'label': '1152.156064.576.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '576.f1.a1', 'projective_image': '1152.156064', '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: 60983644
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.k1', '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.n1.a1'], 'contains': ['24.h1.a1', '24.k1.a1', '24.bc1.a1', '24.be1.a1', '24.bm1.a1', '24.ci1.a1', '24.ck1.a1', '24.cy1.a1', '24.da1.a1', '36.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6443, -1, 2088, -1, 7874, -1, 8066, -1], 'generators': [1, 384, 8, 4, 48, 672], 'label': '1152.156064.12.k1.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.k1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983645
    {'ambient': '1152.156064', 'aut_centralizer_order': 256, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.k1.b1', '288.f1.a1', '288.o1.b1', '288.r1.b1', '288.v1.a1', '288.z1.a1', '288.bf1.b1', '288.bg1.b1', '288.bh1.b1', '288.bh1.b2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1700, -1, 8354, -1, 1930, -1, 1421, -1], 'generators': [152], 'label': '1152.156064.576.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '576.f1.b1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983646
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.l1.a1', '288.g1.a1', '288.q1.a1', '288.s1.a1', '288.x1.a1', '288.x1.b1', '288.y1.a1', '288.ba1.a1', '288.bg1.a1', '288.bg1.b1', '288.bh1.a1', '288.bh1.a2', '288.bh1.b1', '288.bh1.b2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1581, -1, 8218, -1, 1885, -1, 1447, -1], 'generators': [99], 'label': '1152.156064.576.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bp1.a1', 'old_label': '576.g1.a1', 'projective_image': '1152.156064', '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: 60983647
    {'ambient': '1152.156064', 'aut_centralizer_order': 384, 'aut_label': '576.h1', '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.m1.a1', '192.n1.a1', '288.h1.a1', '288.t1.a1', '288.w1.a1', '288.w1.b1', '288.bb1.a1', '288.bg1.a1', '288.bg1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1296, -1, 8384, -1, 1736, -1, 1488, -1], 'generators': [51], 'label': '1152.156064.576.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '576.h1.a1', 'projective_image': '1152.156064', '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: 60983648
    {'ambient': '1152.156064', 'aut_centralizer_order': 128, 'aut_label': '576.i1', '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.i1.a1', '288.t1.a1', '288.u1.a1', '288.x1.a1', '288.x1.b1', '288.bb1.a1', '288.bc1.a1', '288.bf1.a1', '288.bf1.b1', '288.bh1.a1', '288.bh1.a2', '288.bh1.b1', '288.bh1.b2'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1672, -1, 8093, -1, 1854, -1, 1397, -1], 'generators': [147], 'label': '1152.156064.576.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '576.i1.a1', 'projective_image': '1152.156064', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60983649
    {'ambient': '1152.156064', '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.c1.b1', '576.d1.a1', '576.e1.a1', '576.f1.a1', '576.f1.b1', '576.g1.a1', '576.h1.a1', '576.i1.a1'], 'contains': [], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1305, 7272, 8156, 2703, 1778, 3978, 1433, 3310], 'generators': [], 'label': '1152.156064.1152.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': '1152.156064', '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: 60983650
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.o1.a1'], 'contains': ['24.h1.a1', '24.bf1.a1', '24.bi1.a1', '24.cj1.a1', '24.cz1.a1', '36.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9312, -1, 1680, -1, 8369, -1, 7408, -1], 'generators': [2, 384, 8, 48, 672, 4], 'label': '1152.156064.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983651
    {'ambient': '1152.156064', 'aut_centralizer_order': 16, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.o1.a1'], 'contains': ['24.h1.a1', '24.bg1.a1', '24.bh1.a1', '24.cl1.a1', '24.db1.a1', '36.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8718, -1, 638, -1, 7640, -1, 8750, -1], 'generators': [578, 384, 8, 48, 672, 676], 'label': '1152.156064.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983652
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.n1', '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.i1.a1', '24.j1.a1', '24.k1.a1', '24.bj1.a1', '24.bk1.a1', '24.bn1.a1', '24.bo1.a1', '36.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5731, -1, 3615, -1, 4489, -1, 5759, -1], 'generators': [1, 384, 672, 580, 48, 8], 'label': '1152.156064.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.n1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983653
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.o1.a1', '24.q1.a1', '24.s1.a1', '24.w1.a1', '24.y1.a1', '24.cm1.a1', '24.cn1.a1', '24.cn1.a2', '24.cu1.a1', '24.cu1.a2', '24.cx1.a1', '24.cx1.a2', '36.j1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2938, -1, 5940, -1, 3804, -1, 3931, -1], 'generators': [3, 384, 8, 580, 624, 96], 'label': '1152.156064.12.o1.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': '12.o1.a1', 'projective_image': '576.8353', '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': '24.14'}
  • id: 60983654
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.p1', '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.h1.a1'], 'contains': ['24.l1.a1', '24.n1.a1', '24.p1.a1', '24.r1.a1', '24.ba1.a1', '24.cn1.a1', '24.cn1.a2', '24.co1.a1', '24.cw1.a1', '36.k1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4528, -1, 5746, -1, 5345, -1, 4254, -1], 'generators': [3, 384, 8, 4, 624, 96], 'label': '1152.156064.12.p1.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.p1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983655
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.a1', '6.p1.a1'], 'contains': ['24.p1.a1', '24.bb1.a1', '24.bg1.a1', '36.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8219, -1, 3047, -1, 7114, -1, 6177, -1], 'generators': [577, 8, 672, 578, 384, 4], 'label': '1152.156064.12.q1.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.q1.a1', 'projective_image': '576.8353', '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': '32.46'}
  • id: 60983656
    {'ambient': '1152.156064', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.c1.a1', '576.f1.a1', '576.c1.b1', '576.f1.b1', '576.e1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '6.u1.a1', '6.w1.a1', '8.n1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5196, 6299, 4289, 6227, 2431, 4999, 3370, 3421], 'generators': [17, 32, 384, 2, 8, 576, 672, 12], 'label': '1152.156064.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '576.8353', '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': '576.8353'}
  • id: 60983657
    {'ambient': '1152.156064', 'aut_centralizer_order': 24, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.p1.a1'], 'contains': ['24.p1.a1', '24.bc1.a1', '24.bf1.a1', '24.cp1.a1', '24.dc1.a1', '36.m1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8565, -1, 1620, -1, 7959, -1, 7933, -1], 'generators': [1, 8, 4, 2, 672, 384], 'label': '1152.156064.12.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': '576.8353', '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: 60983658
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.s1', '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.p1.a1', '24.bd1.a1', '24.bh1.a1', '36.n1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7792, -1, 2799, -1, 6763, -1, 6349, -1], 'generators': [113, 384, 8, 114, 4, 576], 'label': '1152.156064.12.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': '576.8353', '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: 60983659
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.t1', '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.g1.a1', '6.q1.a1'], 'contains': ['24.p1.a1', '24.be1.a1', '24.bi1.a1', '24.cq1.a1', '24.dd1.a1', '36.o1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8643, -1, 2014, -1, 8278, -1, 7331, -1], 'generators': [17, 384, 8, 18, 576, 4], 'label': '1152.156064.12.t1.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.t1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983677
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.bk1', '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.h1.a1', '6.w1.a1'], 'contains': ['24.ba1.a1', '24.bd1.a1', '24.bf1.a1', '36.bf1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7064, -1, 2631, -1, 6971, -1, 6413, -1], 'generators': [625, 384, 8, 2, 676, 672], 'label': '1152.156064.12.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': '576.8353', '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': '96.209'}
  • id: 60983660
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.u1', '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.i1.a1', '6.j1.a1'], 'contains': ['24.q1.a1', '24.r1.a1', '24.v1.a1', '24.x1.a1', '24.z1.a1', '24.cu1.a1', '24.cu1.a2', '24.cv1.a1', '24.cw1.a1', '36.p1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5354, -1, 5665, -1, 5428, -1, 4623, -1], 'generators': [579, 384, 8, 4, 624, 96], 'label': '1152.156064.12.u1.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.u1.a1', 'projective_image': '576.8353', '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': '48.38'}
  • id: 60983661
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.v1', '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.n1.a1'], 'contains': ['24.r1.a1', '24.t1.a1', '24.bb1.a1', '24.be1.a1', '24.bn1.a1', '36.q1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6666, -1, 3298, -1, 5563, -1, 6021, -1], 'generators': [577, 384, 672, 4, 624, 680], 'label': '1152.156064.12.v1.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.v1.a1', 'projective_image': '576.8353', '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: 60983662
    {'ambient': '1152.156064', '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.h1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.r1.a1', '24.u1.a1', '24.bc1.a1', '24.bd1.a1', '24.bo1.a1', '36.r1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6380, -1, 3510, -1, 5504, -1, 6290, -1], 'generators': [1, 384, 672, 4, 624, 8], 'label': '1152.156064.12.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': '576.8353', '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: 60983663
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.r1.a1', '24.bf1.a1', '24.bh1.a1', '36.s1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9204, -1, 1486, -1, 7166, -1, 8016, -1], 'generators': [2, 384, 8, 624, 4, 672], 'label': '1152.156064.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.x1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983664
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.r1.a1', '24.bg1.a1', '24.bi1.a1', '36.t1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8902, -1, 1511, -1, 7320, -1, 7985, -1], 'generators': [578, 384, 8, 624, 676, 672], 'label': '1152.156064.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983665
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.z1', '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.s1.a1', '24.t1.a1', '24.u1.a1', '24.bj1.a1', '24.bk1.a1', '24.bl1.a1', '24.bm1.a1', '36.u1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5460, -1, 3267, -1, 4540, -1, 5715, -1], 'generators': [1, 384, 672, 580, 624, 8], 'label': '1152.156064.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.z1.a1', 'projective_image': '576.8353', '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': '48.51'}
  • id: 60983666
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '6.p1.a1'], 'contains': ['24.x1.a1', '24.bb1.a1', '24.bf1.a1', '36.v1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8047, -1, 2955, -1, 7269, -1, 6232, -1], 'generators': [577, 8, 672, 2, 384, 676], 'label': '1152.156064.12.ba1.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.ba1.a1', 'projective_image': '576.8353', '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': '32.46'}
  • id: 60983667
    {'ambient': '1152.156064', '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': '288.d1.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.u1.a1', '9.a1.a1', '12.cf1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5274, -1, 4532, -1, 2231, -1, 3308, -1], 'generators': [1, 8, 32, 2, 4, 576, 672, 48], 'label': '1152.156064.3.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': '576.8353', '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': '96.195'}
  • id: 60983668
    {'ambient': '1152.156064', 'aut_centralizer_order': 12, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.p1.a1'], 'contains': ['24.x1.a1', '24.bc1.a1', '24.bg1.a1', '24.de1.a1', '24.de1.a2', '36.w1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7536, -1, 1077, -1, 7789, -1, 8678, -1], 'generators': [1, 8, 676, 578, 672, 384], 'label': '1152.156064.12.bb1.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.bb1.a1', 'projective_image': '576.8353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60983669
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.bc1', '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.x1.a1', '24.bd1.a1', '24.bi1.a1', '36.x1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7233, -1, 2694, -1, 7046, -1, 6544, -1], 'generators': [113, 384, 8, 18, 580, 576], 'label': '1152.156064.12.bc1.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.bc1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983670
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.bd1', '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.f1.a1', '6.i1.a1', '6.q1.a1'], 'contains': ['24.x1.a1', '24.be1.a1', '24.bh1.a1', '24.df1.a1', '24.df1.a2', '36.y1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7863, -1, 1142, -1, 7549, -1, 8488, -1], 'generators': [17, 384, 8, 114, 576, 580], 'label': '1152.156064.12.bd1.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.bd1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983671
    {'ambient': '1152.156064', 'aut_centralizer_order': 8, 'aut_label': '12.be1', '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.v1.a1'], 'contains': ['24.z1.a1', '24.bb1.a1', '24.bh1.a1', '36.z1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8507, -1, 2996, -1, 6905, -1, 6127, -1], 'generators': [161, 384, 8, 114, 4, 576], 'label': '1152.156064.12.be1.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.be1.a1', 'projective_image': '576.8353', '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: 60983672
    {'ambient': '1152.156064', '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': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1', '6.v1.a1'], 'contains': ['24.z1.a1', '24.bc1.a1', '24.bi1.a1', '24.di1.a1', '24.dk1.a1', '36.ba1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8311, -1, 2203, -1, 8131, -1, 7658, -1], 'generators': [65, 384, 8, 18, 576, 4], 'label': '1152.156064.12.bf1.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.bf1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983673
    {'ambient': '1152.156064', '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.c1.a1', '6.j1.a1', '6.w1.a1'], 'contains': ['24.z1.a1', '24.bd1.a1', '24.bg1.a1', '36.bb1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7973, -1, 2747, -1, 6838, -1, 6480, -1], 'generators': [625, 384, 8, 578, 4, 672], 'label': '1152.156064.12.bg1.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.bg1.a1', 'projective_image': '576.8353', '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: 60983674
    {'ambient': '1152.156064', '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.d1.a1', '6.i1.a1', '6.w1.a1'], 'contains': ['24.z1.a1', '24.be1.a1', '24.bf1.a1', '24.dj1.a1', '24.dl1.a1', '36.bc1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9042, -1, 1568, -1, 8196, -1, 7530, -1], 'generators': [49, 384, 8, 2, 672, 4], 'label': '1152.156064.12.bh1.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.bh1.a1', 'projective_image': '576.8353', '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: 60983675
    {'ambient': '1152.156064', 'aut_centralizer_order': 4, 'aut_label': '12.bi1', '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.v1.a1'], 'contains': ['24.ba1.a1', '24.bb1.a1', '24.bi1.a1', '36.bd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7594, -1, 2914, -1, 7210, -1, 5979, -1], 'generators': [161, 384, 8, 18, 580, 576], 'label': '1152.156064.12.bi1.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.bi1.a1', 'projective_image': '576.8353', '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': '96.209'}
  • id: 60983676
    {'ambient': '1152.156064', '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.f1.a1', '6.h1.a1', '6.v1.a1'], 'contains': ['24.ba1.a1', '24.bc1.a1', '24.bh1.a1', '24.dm1.a1', '24.dm1.a2', '36.be1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7004, -1, 1355, -1, 7467, -1, 8558, -1], 'generators': [65, 384, 8, 114, 576, 580], 'label': '1152.156064.12.bj1.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.bj1.a1', 'projective_image': '576.8353', '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'}