Abstract group data - 144.193

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 2, 12, 24], [1, 2, 12, 120], [1, 3, 12, 24], [1, 10, 72, 60], [1, 2, 84, 108], [7, 9, 12, 24], [1, 50, 12, 24], [1, 86, 12, 24], [1, 74, 12, 24]], 'aut_group': '864.4673', 'aut_hash': 4673, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 864, 'aut_permdeg': 10, 'aut_perms': [379560, 374400, 5, 3, 1905840, 1941120, 23, 7], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 1, 1], [2, 3, 3, 1], [3, 1, 2, 1], [3, 4, 6, 1], [6, 1, 6, 1], [6, 3, 2, 1], [6, 3, 6, 1], [6, 4, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times S_3^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '36.10', 'autcent_hash': 10, 'autcent_nilpotent': False, 'autcent_order': 36, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [3, 1, 2], [3, 4, 6], [6, 1, 6], [6, 3, 8], [6, 4, 18]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '12.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 193, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['2.1', 2], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [3, 1, 2, 1], [3, 4, 2, 3], [6, 1, 2, 3], [6, 3, 2, 4], [6, 4, 2, 9]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4, 'exponent': 6, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '144.193', 'hash': 193, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 3, 2, 2], 'inner_gens': [[1, 2, 12, 24], [1, 2, 84, 108], [1, 74, 12, 24], [1, 86, 12, 24]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'A_4', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 36], [3, 12]], 'label': '144.193', 'linC_count': 144, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 18, 'linQ_dim': 5, 'linQ_dim_count': 18, 'linR_count': 18, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2:C6^2', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 48, 'number_divisions': 28, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 98, 'number_subgroups': 234, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 15], [3, 26], [6, 102]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 10, 72, 108], [7, 58, 72, 60], [7, 5, 72, 60]], 'outer_group': '72.46', 'outer_hash': 46, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 8, 'outer_perms': [744, 5761, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 16], [3, 4], [6, 4]], 'representations': {'PC': {'code': 25221789117966582921, 'gens': [1, 2, 4, 5], 'pres': [6, -2, -2, -3, -2, 2, -3, 31, 1017, 447, 1630, 286, 88]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [140827878942, 48233790121]}, 'GLFq': {'d': 3, 'q': 4, 'gens': [164358, 184618, 127769, 56040, 41268, 197379]}, 'Perm': {'d': 11, 'gens': [3669120, 7983360, 843, 840, 7, 16]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 6], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2:C_6^2', 'transitive_degree': 36, '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: 48354688
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 193, 'group_order': 144, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 48354699
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 193, 'group_order': 144, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1, 'size': 1}
  • id: 48354710
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 193, 'group_order': 144, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 6, 'size': 1}
  • id: 48354721
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 193, 'group_order': 144, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 7, 'size': 1}
  • id: 48354731
    {'aut_label': '2D', 'centralizer': '3.a1.a1', 'counter': 5, 'group_counter': 193, 'group_order': 144, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 72, 'size': 3}
  • id: 48354732
    {'aut_label': '2E', 'centralizer': '3.a1.a1', 'counter': 6, 'group_counter': 193, 'group_order': 144, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 73, 'size': 3}
  • id: 48354733
    {'aut_label': '2E', 'centralizer': '3.a1.a1', 'counter': 7, 'group_counter': 193, 'group_order': 144, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 78, 'size': 3}
  • id: 48354734
    {'aut_label': '2E', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 193, 'group_order': 144, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 79, 'size': 3}
  • id: 48354735
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 193, 'group_order': 144, 'label': '3A1', 'order': 3, 'powers': [10, 1], 'representative': 96, 'size': 1}
  • id: 48354689
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 193, 'group_order': 144, 'label': '3A-1', 'order': 3, 'powers': [9, 1], 'representative': 48, 'size': 1}
  • id: 48354690
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 11, 'group_counter': 193, 'group_order': 144, 'label': '3B1', 'order': 3, 'powers': [12, 1], 'representative': 4, 'size': 4}
  • id: 48354691
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 12, 'group_counter': 193, 'group_order': 144, 'label': '3B-1', 'order': 3, 'powers': [11, 1], 'representative': 8, 'size': 4}
  • id: 48354692
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 13, 'group_counter': 193, 'group_order': 144, 'label': '3C1', 'order': 3, 'powers': [14, 1], 'representative': 100, 'size': 4}
  • id: 48354693
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 14, 'group_counter': 193, 'group_order': 144, 'label': '3C-1', 'order': 3, 'powers': [13, 1], 'representative': 56, 'size': 4}
  • id: 48354694
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 15, 'group_counter': 193, 'group_order': 144, 'label': '3D1', 'order': 3, 'powers': [16, 1], 'representative': 136, 'size': 4}
  • id: 48354695
    {'aut_label': '3B1', 'centralizer': '4.b1.a1', 'counter': 16, 'group_counter': 193, 'group_order': 144, 'label': '3D-1', 'order': 3, 'powers': [15, 1], 'representative': 32, 'size': 4}
  • id: 48354696
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 193, 'group_order': 144, 'label': '6A1', 'order': 6, 'powers': [9, 2], 'representative': 49, 'size': 1}
  • id: 48354697
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 193, 'group_order': 144, 'label': '6A-1', 'order': 6, 'powers': [10, 2], 'representative': 97, 'size': 1}
  • id: 48354698
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 193, 'group_order': 144, 'label': '6B1', 'order': 6, 'powers': [9, 3], 'representative': 54, 'size': 1}
  • id: 48354700
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 193, 'group_order': 144, 'label': '6B-1', 'order': 6, 'powers': [10, 3], 'representative': 102, 'size': 1}
  • id: 48354701
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 193, 'group_order': 144, 'label': '6C1', 'order': 6, 'powers': [9, 4], 'representative': 55, 'size': 1}
  • id: 48354702
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 193, 'group_order': 144, 'label': '6C-1', 'order': 6, 'powers': [10, 4], 'representative': 103, 'size': 1}
  • id: 48354703
    {'aut_label': '6D1', 'centralizer': '3.a1.a1', 'counter': 23, 'group_counter': 193, 'group_order': 144, 'label': '6D1', 'order': 6, 'powers': [10, 5], 'representative': 24, 'size': 3}
  • id: 48354704
    {'aut_label': '6D1', 'centralizer': '3.a1.a1', 'counter': 24, 'group_counter': 193, 'group_order': 144, 'label': '6D-1', 'order': 6, 'powers': [9, 5], 'representative': 60, 'size': 3}
  • id: 48354705
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 25, 'group_counter': 193, 'group_order': 144, 'label': '6E1', 'order': 6, 'powers': [10, 6], 'representative': 25, 'size': 3}
  • id: 48354706
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 26, 'group_counter': 193, 'group_order': 144, 'label': '6E-1', 'order': 6, 'powers': [9, 6], 'representative': 61, 'size': 3}
  • id: 48354707
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 27, 'group_counter': 193, 'group_order': 144, 'label': '6F1', 'order': 6, 'powers': [10, 7], 'representative': 30, 'size': 3}
  • id: 48354708
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 28, 'group_counter': 193, 'group_order': 144, 'label': '6F-1', 'order': 6, 'powers': [9, 7], 'representative': 66, 'size': 3}
  • id: 48354709
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 29, 'group_counter': 193, 'group_order': 144, 'label': '6G1', 'order': 6, 'powers': [10, 8], 'representative': 31, 'size': 3}
  • id: 48354711
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 30, 'group_counter': 193, 'group_order': 144, 'label': '6G-1', 'order': 6, 'powers': [9, 8], 'representative': 67, 'size': 3}
  • id: 48354712
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 31, 'group_counter': 193, 'group_order': 144, 'label': '6H1', 'order': 6, 'powers': [11, 3], 'representative': 2, 'size': 4}
  • id: 48354713
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 32, 'group_counter': 193, 'group_order': 144, 'label': '6H-1', 'order': 6, 'powers': [12, 3], 'representative': 10, 'size': 4}
  • id: 48354714
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 33, 'group_counter': 193, 'group_order': 144, 'label': '6I1', 'order': 6, 'powers': [13, 3], 'representative': 50, 'size': 4}
  • id: 48354715
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 34, 'group_counter': 193, 'group_order': 144, 'label': '6I-1', 'order': 6, 'powers': [14, 3], 'representative': 34, 'size': 4}
  • id: 48354716
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 35, 'group_counter': 193, 'group_order': 144, 'label': '6J1', 'order': 6, 'powers': [15, 3], 'representative': 26, 'size': 4}
  • id: 48354717
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 36, 'group_counter': 193, 'group_order': 144, 'label': '6J-1', 'order': 6, 'powers': [16, 3], 'representative': 58, 'size': 4}
  • id: 48354718
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 37, 'group_counter': 193, 'group_order': 144, 'label': '6K1', 'order': 6, 'powers': [12, 2], 'representative': 5, 'size': 4}
  • id: 48354719
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 38, 'group_counter': 193, 'group_order': 144, 'label': '6K-1', 'order': 6, 'powers': [11, 2], 'representative': 9, 'size': 4}
  • id: 48354720
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 39, 'group_counter': 193, 'group_order': 144, 'label': '6L1', 'order': 6, 'powers': [11, 4], 'representative': 3, 'size': 4}
  • id: 48354722
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 40, 'group_counter': 193, 'group_order': 144, 'label': '6L-1', 'order': 6, 'powers': [12, 4], 'representative': 11, 'size': 4}
  • id: 48354723
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 41, 'group_counter': 193, 'group_order': 144, 'label': '6M1', 'order': 6, 'powers': [16, 2], 'representative': 53, 'size': 4}
  • id: 48354724
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 42, 'group_counter': 193, 'group_order': 144, 'label': '6M-1', 'order': 6, 'powers': [15, 2], 'representative': 33, 'size': 4}
  • id: 48354725
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 43, 'group_counter': 193, 'group_order': 144, 'label': '6N1', 'order': 6, 'powers': [14, 2], 'representative': 29, 'size': 4}
  • id: 48354726
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 44, 'group_counter': 193, 'group_order': 144, 'label': '6N-1', 'order': 6, 'powers': [13, 2], 'representative': 57, 'size': 4}
  • id: 48354727
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 45, 'group_counter': 193, 'group_order': 144, 'label': '6O1', 'order': 6, 'powers': [13, 4], 'representative': 51, 'size': 4}
  • id: 48354728
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 46, 'group_counter': 193, 'group_order': 144, 'label': '6O-1', 'order': 6, 'powers': [14, 4], 'representative': 35, 'size': 4}
  • id: 48354729
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 47, 'group_counter': 193, 'group_order': 144, 'label': '6P1', 'order': 6, 'powers': [15, 4], 'representative': 27, 'size': 4}
  • id: 48354730
    {'aut_label': '6H1', 'centralizer': '4.b1.a1', 'counter': 48, 'group_counter': 193, 'group_order': 144, 'label': '6P-1', 'order': 6, 'powers': [16, 4], 'representative': 59, 'size': 4}
• 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: 118423
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 118434
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 118444
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 118445
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 118446
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, 2], 'schur_index': 1}
  • id: 118447
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 118448
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1g', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 118449
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1h', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 118450
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 2, 1, -2, -1, 1, 1, -1, 1, -1, -2, 1, 1, 1, 1, -2, -2, -1, 2], 'schur_index': 1}
  • id: 118424
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -2, -2, 2, 1, 2, 1, 1, 1, -2, -2, 1, 1, -1, -1], 'schur_index': 1}
  • id: 118425
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -2, 1, 2, 1, 1, -1, -2, -1, 1, -2, -2, 1, 1, 1, 1, 2, -1], 'schur_index': 1}
  • id: 118426
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, 2, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 118427
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, -1, -1, -1, -1, 2, -1, -1, 2, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -2, -1, 2, 1, -1, -1, 1, -1, 1, -2, 1, 1, 1, 1, -2, 2, 1, -2], 'schur_index': 1}
  • id: 118428
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, -1, -1, -1, 2, -1, -1, 2, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 2, 2, -2, -1, -2, 1, 1, 1, -2, -2, 1, -1, 1, 1], 'schur_index': 1}
  • id: 118429
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 2, -1, -2, -1, -1, 1, 2, 1, 1, -2, -2, 1, 1, 1, -1, -2, 1], 'schur_index': 1}
  • id: 118430
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 118431
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1q', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 2, -1, -1, -1, -1, 2, -2, 1, -2], 'schur_index': 1}
  • id: 118432
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1r', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, -2, -1, -1, -1, 2, 2, -1, 1, 1, 1], 'schur_index': 1}
  • id: 118433
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1s', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, 1, -1, 2, 2, -1, -1, -1, 1, -2, 1], 'schur_index': 1}
  • id: 118435
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.1t', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 118436
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118437
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3b', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -1, 1, 1, -1, 3, 3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 3, 3, 1, 1, 1, -1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118438
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3c', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, -3, 3, -3, -1, 1, -1, 1, 3, 3, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, -3, -3, 1, -1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118439
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3d', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, -1, 1, 1, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, -3, -3, -1, 1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118440
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3e', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118441
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3f', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -2, 2, 2, -2, -3, -3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -3, -3, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118442
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3g', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, -6, 6, -6, -2, 2, -2, 2, -3, -3, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 3, 3, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 118443
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '144.193', 'group_order': 144, 'image': None, 'label': '144.193.3h', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, 2, 2, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, 3, 3, 1, -1, 1, 1, 1, -1, -1, -1, 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: 126900
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 144, 'label': '144.193.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 126911
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.c1', 'kernel_order': 72, 'label': '144.193.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 126922
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 72, 'label': '144.193.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 126933
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 72, 'label': '144.193.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 126943
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 48, 'label': '144.193.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]]]}
  • id: 126944
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 48, 'label': '144.193.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]]]}
  • id: 126945
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 48, 'label': '144.193.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 126946
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 48, 'label': '144.193.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 126947
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 48, 'label': '144.193.1g1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]]]}
  • id: 126901
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 48, 'label': '144.193.1g2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]]]}
  • id: 126902
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 48, 'label': '144.193.1h1', 'nt': [3, 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, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]]]}
  • id: 126903
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 48, 'label': '144.193.1h2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]]]}
  • id: 126904
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.g1', 'kernel_order': 24, 'label': '144.193.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 0]]]}
  • id: 126905
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.g1', 'kernel_order': 24, 'label': '144.193.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]]]}
  • id: 126906
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.i1', 'kernel_order': 24, 'label': '144.193.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 126907
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.i1', 'kernel_order': 24, 'label': '144.193.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 126908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.h1', 'kernel_order': 24, 'label': '144.193.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 1]]]}
  • id: 126909
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.h1', 'kernel_order': 24, 'label': '144.193.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, -1]]]}
  • id: 126910
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.c1', 'kernel_order': 24, 'label': '144.193.1l1', 'nt': [6, 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, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]]]}
  • id: 126912
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.c1', 'kernel_order': 24, 'label': '144.193.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]]]}
  • id: 126913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.d1', 'kernel_order': 24, 'label': '144.193.1m1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 0]]]}
  • id: 126914
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.d1', 'kernel_order': 24, 'label': '144.193.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]]]}
  • id: 126915
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.f1', 'kernel_order': 24, 'label': '144.193.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 126916
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.f1', 'kernel_order': 24, 'label': '144.193.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 126917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.e1', 'kernel_order': 24, 'label': '144.193.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[-1, 1]]]}
  • id: 126918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.e1', 'kernel_order': 24, 'label': '144.193.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, -1]]]}
  • id: 126919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 27, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 24, 'label': '144.193.1p1', 'nt': [6, 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, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]]]}
  • id: 126920
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 28, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 24, 'label': '144.193.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]]]}
  • id: 126921
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 29, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 24, 'label': '144.193.1q1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]]]}
  • id: 126923
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 30, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 24, 'label': '144.193.1q2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]]]}
  • id: 126924
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 31, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 24, 'label': '144.193.1r1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 126925
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 32, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 24, 'label': '144.193.1r2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 126926
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 33, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 24, 'label': '144.193.1s1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]]]}
  • id: 126927
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 34, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 24, 'label': '144.193.1s2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]]]}
  • id: 126928
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 35, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 24, 'label': '144.193.1t1', 'nt': [6, 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, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
  • id: 126929
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 144, 'counter': 36, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 24, 'label': '144.193.1t2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
  • id: 126930
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 12, 'label': '144.193.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 126931
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.c1', 'kernel_order': 6, 'label': '144.193.3b', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 126932
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.b1', 'kernel_order': 6, 'label': '144.193.3c', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 126934
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 6, 'label': '144.193.3d', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 126935
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 41, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 4, 'label': '144.193.3e1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126936
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 42, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 4, 'label': '144.193.3e2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126937
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 43, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.c1', 'kernel_order': 2, 'label': '144.193.3f1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126938
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 44, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.c1', 'kernel_order': 2, 'label': '144.193.3f2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126939
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 45, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 2, 'label': '144.193.3g1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126940
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 46, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 2, 'label': '144.193.3g2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126941
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 47, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 2, 'label': '144.193.3h1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 126942
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 12, 'counter': 48, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '144.193', 'group_counter': 193, 'group_order': 144, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 2, 'label': '144.193.3h2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 11701185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 144, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '144.193.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 11701196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.2.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': ['C1'], 'split': True, '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: 11701207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 11701218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.c1', '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 11701229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, '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: 11701240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.3.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.3.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.3.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 36, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': 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: 11701186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701187
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701188
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701189
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.6.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 14, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 15, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 16, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 17, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 20, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 22, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.6.b1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 11701200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.6.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701204
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701205
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.a1.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.8.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '144.193.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 2}
  • id: 11701209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 31, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], '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: 11701210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], '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: 11701211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 33, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.12.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': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 11701212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 34, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 11701213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 35, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.12.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 11701214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701225
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701226
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.12.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '144.193.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 11701231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.18.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.18.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.18.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.18.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 11701238
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 58, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701239
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 59, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701241
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 60, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.24.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701242
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': 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: 11701243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': 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: 11701244
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701245
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701246
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701247
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701248
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701249
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701250
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.b1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701252
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701253
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 11701254
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701255
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.24.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 11701256
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '144.193.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '144.193.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], '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: 11701258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701263
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701264
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701265
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '144.193.36.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 11701270
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 3, 'counter': 87, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.49', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times A_4', 'simple': True, 'solvable': True, 'special_labels': ['C4'], '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: 11701271
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, '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: 11701272
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, '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: 11701274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.48.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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: 11701275
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 11701276
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 11701277
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '144.193.72.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 11701278
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 11701279
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 11701280
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, '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: 11701281
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '144.193.72.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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: 11701282
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '144.193', 'ambient_counter': 193, 'ambient_order': 144, 'ambient_tex': 'C_2^2:C_6^2', 'central': True, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 1, 'counter': 98, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '144.193.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '144.193', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 193, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:C_6^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C5'], '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: 11701206
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.c1', '24.b1.g1', '24.b1.h1', '24.b1.i1'], 'core': '24.a1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1258, -1, 993, -1, 1382, -1, 2687, -1], 'generators': [7, 4, 48], 'label': '144.193.8.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.c1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701185
    {'ambient': '144.193', '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': '12.a1.a1', 'complements': ['144.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.a1.c1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1', '4.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2838, 6434, 2856, 4936, 2657, 5859, 2494, 4796], 'generators': [1, 72, 84, 6, 4, 48], 'label': '144.193.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.c1', '2.a1.b1', '3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '12.3', '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': '12.3'}
  • id: 11701186
    {'ambient': '144.193', 'aut_centralizer_order': 3, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 12, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.a1.c1', '12.a1.a1', '12.f1.a1', '12.f1.b1', '12.f1.c1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1347, -1, 1085, -1, 2863, -1, 2107, -1], 'generators': [1, 6, 4, 48], 'label': '144.193.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '12.3', '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': '1.1'}
  • id: 11701187
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': ['24.b1.d1', '24.b1.f1', '24.b1.e1', '24.b1.g1', '24.b1.i1', '24.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.g1.a1', '18.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6456, 6105, 6360, 1966, 4597, 6207, 5201, 2033], 'generators': [1, 12, 72, 48], 'label': '144.193.6.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '24.13', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701188
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': ['24.b1.a1', '24.b1.c1', '24.b1.b1', '24.b1.g1', '24.b1.i1', '24.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.b1', '12.g1.b1', '18.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6456, 6105, 5594, 1162, 4597, 6207, 4779, 369], 'generators': [6, 12, 72, 48], 'label': '144.193.6.a1.b1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.b1', '24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '24.13', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701189
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': ['24.b1.d1', '24.b1.f1', '24.b1.e1', '24.b1.a1', '24.b1.c1', '24.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.c1', '12.g1.c1', '18.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6456, 6105, 5977, 356, 4597, 6207, 5622, 1201], 'generators': [7, 12, 72, 48], 'label': '144.193.6.a1.c1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '6.a1.c1', 'normal_contained_in': ['2.a1.c1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.c1', '24.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.c1', 'projective_image': '24.13', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.a1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701190
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.f1', '24.b1.e1', '24.a1.c1', '24.d1.c1', '24.b1.i1', '24.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '24.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 2329, 9644, 1327, 3537, 520, 9690], 'generators': [1, 4, 12, 72], 'label': '144.193.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.b1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701191
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.d1', '24.b1.f1', '24.a1.c1', '24.d1.c1', '24.b1.g1', '24.b1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['12.c1.b1', '18.a1.a1', '24.b1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 3877, 4895, 1327, 3537, 2400, 8258], 'generators': [1, 100, 12, 72], 'label': '144.193.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1', '3.b1.b1'], 'normal_contains': ['12.c1.b1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701192
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.e1', '24.b1.d1', '24.a1.c1', '24.d1.c1', '24.b1.h1', '24.b1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['12.c1.c1', '18.a1.a1', '24.b1.c1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 4865, 7172, 1327, 3537, 3697, 6111], 'generators': [1, 52, 12, 72], 'label': '144.193.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1', '3.b1.c1'], 'normal_contains': ['12.c1.c1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701193
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.a1', '24.d1.a1', '24.b1.c1', '24.b1.b1', '24.a1.c1', '24.d1.c1', '24.b1.i1', '24.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.a1.b1', '24.b1.d1'], 'core': '6.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 1483, 8557, 1327, 3537, 157, 7543], 'generators': [6, 4, 12, 72], 'label': '144.193.6.b1.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.d1', 'normal_contained_in': ['2.a1.b1', '3.b1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.d1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701194
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.a1', '24.d1.a1', '24.b1.a1', '24.b1.c1', '24.a1.c1', '24.d1.c1', '24.b1.g1', '24.b1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.b1'], 'contains': ['12.c1.b1', '18.a1.b1', '24.b1.e1'], 'core': '6.b1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 3031, 4002, 1327, 3537, 1452, 3964], 'generators': [6, 100, 12, 72], 'label': '144.193.6.b1.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.e1', 'normal_contained_in': ['2.a1.b1', '3.b1.b1'], 'normal_contains': ['12.c1.b1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.e1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.e1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701195
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.a1', '24.d1.a1', '24.b1.b1', '24.b1.a1', '24.a1.c1', '24.d1.c1', '24.b1.h1', '24.b1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.c1'], 'contains': ['12.c1.c1', '18.a1.b1', '24.b1.f1'], 'core': '6.b1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 4207, 6480, 1327, 3537, 3334, 3248], 'generators': [6, 52, 12, 72], 'label': '144.193.6.b1.f1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.f1', 'normal_contained_in': ['2.a1.b1', '3.b1.c1'], 'normal_contains': ['12.c1.c1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.f1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701196
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['72.a1.b1', '72.c1.b1', '72.a1.c1', '72.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '8.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3153, 3914, 3019, 6407, 1327, 3190, 2298, 6530], 'generators': [1, 72, 4, 48, 84], 'label': '144.193.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.c1', '6.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701197
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.f1', '24.b1.e1', '24.a1.a1', '24.d1.a1', '24.b1.c1', '24.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.a1.c1', '24.b1.g1'], 'core': '6.b1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 1812, 7864, 1327, 3537, 882, 8974], 'generators': [7, 4, 12, 72], 'label': '144.193.6.b1.g1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.g1', 'normal_contained_in': ['2.a1.c1', '3.b1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.g1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.g1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701198
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.d1', '24.b1.f1', '24.a1.a1', '24.d1.a1', '24.b1.a1', '24.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '3.b1.b1'], 'contains': ['12.c1.b1', '18.a1.c1', '24.b1.h1'], 'core': '6.b1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 3360, 3111, 1327, 3537, 2867, 5395], 'generators': [7, 100, 12, 72], 'label': '144.193.6.b1.h1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.h1', 'normal_contained_in': ['2.a1.c1', '3.b1.b1'], 'normal_contains': ['12.c1.b1', '18.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.h1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.h1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701199
    {'ambient': '144.193', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['24.a1.b1', '24.d1.b1', '24.b1.e1', '24.b1.d1', '24.a1.a1', '24.d1.a1', '24.b1.b1', '24.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '3.b1.c1'], 'contains': ['12.c1.c1', '18.a1.c1', '24.b1.i1'], 'core': '6.b1.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 3275, 4536, 5788, 1327, 3537, 4164, 4679], 'generators': [7, 52, 12, 72], 'label': '144.193.6.b1.i1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.i1', 'normal_contained_in': ['2.a1.c1', '3.b1.c1'], 'normal_contains': ['12.c1.c1', '18.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.i1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.i1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701200
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 108, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.g1.b1', '12.g1.c1', '12.h1.a1', '12.h1.a2', '18.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7900, -1, 7733, -1, 7710, -1, 8093, -1], 'generators': [1, 78, 12, 48], 'label': '144.193.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '24.13', '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': '1.1'}
  • id: 11701201
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 108, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.b1', '12.e1.b1', '12.g1.a1', '12.g1.c1', '12.h1.a1', '12.h1.a2', '18.b1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7900, -1, 8937, -1, 7710, -1, 7363, -1], 'generators': [73, 6, 12, 48], 'label': '144.193.6.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701202
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 108, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.c1', '12.e1.c1', '12.g1.a1', '12.g1.b1', '12.h1.a1', '12.h1.a2', '18.b1.c1'], 'core': '24.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7900, -1, 8374, -1, 7710, -1, 8668, -1], 'generators': [73, 78, 12, 48], 'label': '144.193.6.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.c1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701203
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.d1.b1', '12.d1.c1', '12.e1.a1', '12.e1.b1', '12.e1.c1', '18.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5062, -1, 6837, -1, 5674, -1, 6114, -1], 'generators': [1, 6, 12, 48], 'label': '144.193.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '12.3', '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': '1.1'}
  • id: 11701204
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.b1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1258, -1, 1534, -1, 1382, -1, 1559, -1], 'generators': [1, 4, 48], 'label': '144.193.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.13', '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': '1.1'}
  • id: 11701205
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.b1', '24.b1.d1', '24.b1.e1', '24.b1.f1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1258, -1, 568, -1, 1382, -1, 1092, -1], 'generators': [6, 4, 48], 'label': '144.193.8.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.b1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701207
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['72.a1.a1', '72.c1.a1', '72.a1.c1', '72.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.b1', '6.b1.d1', '6.b1.e1', '6.b1.f1', '8.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3153, 3914, 2263, 5603, 1327, 3190, 1814, 4022], 'generators': [6, 72, 4, 48, 84], 'label': '144.193.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.b1', '6.b1.d1', '6.b1.f1', '6.b1.e1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701208
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '9.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 24, 'centralizer': '3.a1.a1', 'complements': ['16.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.a1.c1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '18.c1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5321, 8159, 5943, 3623, 6497, 8400, 4457, 2670], 'generators': [1, 6, 12, 72], 'label': '144.193.9.a1.a1', 'mobius_quo': -2, 'mobius_sub': 3, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normal_contains': ['18.a1.a1', '18.a1.c1', '18.a1.b1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '36.11', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701209
    {'ambient': '144.193', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '1.a1.a1', 'complements': ['12.c1.a1', '12.c1.c1', '12.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.a1.c1', '36.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2634, 8120, 3833, 895, 4179, 8346, 4943, 1095], 'generators': [1, 6, 48], 'label': '144.193.12.a1.a1', 'mobius_quo': -2, 'mobius_sub': 4, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.a1.a1', '24.a1.c1', '24.a1.b1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701210
    {'ambient': '144.193', 'aut_centralizer_order': 72, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': ['12.f1.a1', '12.f1.c1', '12.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.a1.c1'], 'contains': ['24.c1.a1', '36.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4056, 2538, 5174, 1788, 3246, 3665, 4578, 2018], 'generators': [12, 72, 48], 'label': '144.193.12.b1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.c1', '6.a1.b1'], 'normal_contains': ['36.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '48.49', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701211
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.e1.b1', '12.e1.a1', '12.e1.c1', '12.h1.a1', '12.h1.a2', '12.f1.c1', '12.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.d1', '6.b1.g1'], 'contains': ['36.b1.a1', '48.b1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3345, 524, 2146, 9577, 408, 1764, 243, 7543], 'generators': [4, 12, 72], 'label': '144.193.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.g1', '6.b1.d1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '144.193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701212
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.e1.b1', '12.e1.a1', '12.e1.c1', '12.h1.a1', '12.h1.a2', '12.f1.a1', '12.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.b1', '6.b1.e1', '6.b1.h1'], 'contains': ['36.b1.a1', '48.b1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3345, 524, 3302, 5172, 408, 1764, 1838, 5231], 'generators': [100, 12, 72], 'label': '144.193.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.a1.a1', '6.b1.b1', '6.b1.h1', '6.b1.e1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '144.193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701213
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 36, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.e1.b1', '12.e1.a1', '12.e1.c1', '12.h1.a1', '12.h1.a2', '12.f1.b1', '12.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.c1', '6.b1.f1', '6.b1.i1'], 'contains': ['36.b1.a1', '48.b1.c1'], 'core': '12.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3345, 524, 4365, 7787, 408, 1764, 3068, 4764], 'generators': [52, 12, 72], 'label': '144.193.12.c1.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.c1', 'normal_contained_in': ['4.a1.a1', '6.b1.c1', '6.b1.i1', '6.b1.f1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.c1', 'projective_image': '144.193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.c1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701214
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1', '36.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6285, -1, 6340, -1, 5674, -1, 6114, -1], 'generators': [1, 12, 48], 'label': '144.193.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '24.13', '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': '1.1'}
  • id: 11701215
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.c1.b1', '6.d1.a1'], 'contains': ['24.a1.b1', '24.c1.a1', '24.d1.b1', '36.c1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6285, -1, 7003, -1, 5674, -1, 5528, -1], 'generators': [6, 12, 48], 'label': '144.193.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701216
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '6.c1.c1', '6.d1.a1'], 'contains': ['24.a1.c1', '24.c1.a1', '24.d1.c1', '36.c1.c1'], 'core': '24.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6285, -1, 6672, -1, 5674, -1, 6479, -1], 'generators': [7, 12, 48], 'label': '144.193.12.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.c1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701217
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.d1.b1', '24.d1.c1', '36.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7216, -1, 7335, -1, 8101, -1, 8381, -1], 'generators': [1, 18, 48], 'label': '144.193.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701218
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['72.a1.b1', '72.c1.b1', '72.a1.a1', '72.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.c1', '6.b1.g1', '6.b1.h1', '6.b1.i1', '8.a1.c1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3153, 3914, 2690, 4423, 1327, 3190, 3082, 5570], 'generators': [7, 72, 4, 48, 84], 'label': '144.193.2.a1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.c1', '6.b1.g1', '6.b1.i1', '6.b1.h1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.c1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701219
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '6.d1.a1'], 'contains': ['24.a1.b1', '24.d1.a1', '24.d1.c1', '36.d1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7216, -1, 8939, -1, 8101, -1, 7285, -1], 'generators': [13, 6, 48], 'label': '144.193.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701220
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '6.d1.a1'], 'contains': ['24.a1.c1', '24.d1.a1', '24.d1.b1', '36.d1.c1'], 'core': '24.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7216, -1, 8515, -1, 8101, -1, 9111, -1], 'generators': [13, 18, 48], 'label': '144.193.12.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.c1', 'projective_image': '24.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701221
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.b1.a1'], 'contains': ['24.b1.a1', '24.b1.d1', '24.b1.g1', '36.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [404, -1, 161, -1, 2314, -1, 522, -1], 'generators': [1, 6, 4], 'label': '144.193.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '36.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701222
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1', '4.b1.a1'], 'contains': ['24.b1.b1', '24.b1.e1', '24.b1.h1', '36.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [404, -1, 1521, -1, 2314, -1, 2220, -1], 'generators': [1, 6, 100], 'label': '144.193.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.f1.b1', 'projective_image': '36.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701223
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1', '4.b1.a1'], 'contains': ['24.b1.c1', '24.b1.f1', '24.b1.i1', '36.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [404, -1, 2585, -1, 2314, -1, 3450, -1], 'generators': [1, 6, 52], 'label': '144.193.12.f1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.f1.c1', 'projective_image': '36.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701224
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.b1', '6.c1.c1'], 'contains': ['24.c1.a1', '24.d1.a1', '36.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8406, -1, 9934, -1, 7168, -1, 8015, -1], 'generators': [73, 12, 48], 'label': '144.193.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.49', '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': '1.1'}
  • id: 11701225
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.c1.a1', '6.c1.c1'], 'contains': ['24.c1.a1', '24.d1.b1', '36.e1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8406, -1, 7667, -1, 7168, -1, 8746, -1], 'generators': [78, 12, 48], 'label': '144.193.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.b1', 'projective_image': '48.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701226
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '6.c1.a1', '6.c1.b1'], 'contains': ['24.c1.a1', '24.d1.c1', '36.e1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8406, -1, 8090, -1, 7168, -1, 7650, -1], 'generators': [79, 12, 48], 'label': '144.193.12.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.c1', 'projective_image': '48.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701227
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.c1.b1', '6.c1.c1'], 'contains': ['24.d1.a1', '24.d1.b1', '24.d1.c1', '36.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9596, -1, 9272, -1, 9596, -1, 9842, -1], 'generators': [85, 18, 48], 'label': '144.193.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '48.49', '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': '1.1'}
  • id: 11701228
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.c1.b1', '6.c1.c1'], 'contains': ['24.d1.a1', '24.d1.b1', '24.d1.c1', '36.f1.a2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9596, -1, 9603, -1, 9596, -1, 9476, -1], 'generators': [73, 18, 48], 'label': '144.193.12.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a2', 'projective_image': '48.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701229
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 12, 'centralizer': '3.a1.a1', 'complements': ['48.b1.a1', '48.b1.c1', '48.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.a1.c1', '6.c1.a1', '6.c1.b1', '6.c1.c1', '6.d1.a1', '9.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 9476, 6599, 1382, 5674, 8729, 5622, 1620], 'generators': [1, 48, 6, 12, 72], 'label': '144.193.3.a1.a1', 'mobius_quo': 2, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.a1.c1', '6.a1.b1', '9.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '12.3', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701230
    {'ambient': '144.193', 'aut_centralizer_order': 18, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 72, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1', '8.a1.b1', '8.a1.c1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1929, -1, 1010, -1, 1382, -1, 1895, -1], 'generators': [4, 48], 'label': '144.193.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.49', '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': '1.1'}
  • id: 11701231
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': ['8.a1.b1', '8.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.e1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5704, 4962, 5221, 4603, 4926, 5658, 4065, 5639], 'generators': [1, 12, 72], 'label': '144.193.18.a1.a1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.c1', '6.b1.b1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '72.47', 'quotient_action_image': '3.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701232
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': ['8.a1.a1', '8.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.b1.d1', '6.b1.e1', '6.b1.f1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.b1', '36.e1.b1'], 'core': '18.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5704, 4962, 4368, 4182, 4926, 5658, 3845, 3248], 'generators': [6, 12, 72], 'label': '144.193.18.a1.b1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '18.a1.b1', 'normal_contained_in': ['6.a1.b1', '6.b1.d1', '6.b1.f1', '6.b1.e1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.b1', 'projective_image': '72.47', 'quotient_action_image': '3.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701233
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': ['8.a1.b1', '8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '6.b1.g1', '6.b1.h1', '6.b1.i1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.c1', '36.e1.c1'], 'core': '18.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5704, 4962, 4785, 3105, 4926, 5658, 4285, 4356], 'generators': [7, 12, 72], 'label': '144.193.18.a1.c1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '18.a1.c1', 'normal_contained_in': ['6.a1.c1', '6.b1.g1', '6.b1.i1', '6.b1.h1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '72.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.c1', 'projective_image': '72.47', 'quotient_action_image': '3.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '18.a1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701234
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.d1.a1', '36.e1.b1', '36.e1.c1', '36.f1.a1', '36.f1.a2'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8742, -1, 7439, -1, 8848, -1, 6772, -1], 'generators': [1, 78, 12], 'label': '144.193.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '72.47', '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': '1.1'}
  • id: 11701235
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '9.a1.a1'], 'contains': ['36.c1.b1', '36.d1.b1', '36.e1.a1', '36.e1.c1', '36.f1.a1', '36.f1.a2'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8742, -1, 7933, -1, 8848, -1, 5821, -1], 'generators': [73, 6, 12], 'label': '144.193.18.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.b1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701236
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 216, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '9.a1.a1'], 'contains': ['36.c1.c1', '36.d1.c1', '36.e1.a1', '36.e1.b1', '36.f1.a1', '36.f1.a2'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8742, -1, 7733, -1, 8848, -1, 6992, -1], 'generators': [73, 78, 12], 'label': '144.193.18.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.c1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701237
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.c1.b1', '36.c1.c1', '36.d1.a1', '36.d1.b1', '36.d1.c1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5144, -1, 6221, -1, 6421, -1, 5236, -1], 'generators': [1, 6, 12], 'label': '144.193.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '36.11', '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': '1.1'}
  • id: 11701238
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '1.a1.a1', 'complements': ['6.b1.d1', '6.b1.f1', '6.b1.e1', '6.b1.g1', '6.b1.i1', '6.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3140, 6434, 4699, 2151, 5057, 6719, 4857, 2256], 'generators': [1, 48], 'label': '144.193.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': -4, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701239
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '1.a1.a1', 'complements': ['6.b1.a1', '6.b1.c1', '6.b1.b1', '6.b1.g1', '6.b1.i1', '6.b1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.a1.a1', '12.d1.b1', '12.e1.b1'], 'contains': ['48.a1.a1', '72.a1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3140, 6434, 5050, 1347, 5057, 6719, 4443, 1180], 'generators': [6, 48], 'label': '144.193.24.a1.b1', 'mobius_quo': 1, 'mobius_sub': -4, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['6.a1.b1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701240
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['48.a1.a1', '48.b1.c1', '48.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.b1.d1', '6.b1.g1', '9.a1.a1', '12.f1.a1'], 'core': '3.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2490, 6434, 1826, 7608, 2328, 5859, 702, 7543], 'generators': [1, 72, 6, 4, 12], 'label': '144.193.3.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1', '6.b1.g1', '6.b1.d1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.a1', 'projective_image': '36.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701241
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '1.a1.a1', 'complements': ['6.b1.d1', '6.b1.f1', '6.b1.e1', '6.b1.a1', '6.b1.c1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.c1', '12.a1.a1', '12.d1.c1', '12.e1.c1'], 'contains': ['48.a1.a1', '72.a1.c1'], 'core': '24.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3140, 6434, 4875, 956, 5057, 6719, 5271, 1599], 'generators': [7, 48], 'label': '144.193.24.a1.c1', 'mobius_quo': 1, 'mobius_sub': -4, 'normal_closure': '24.a1.c1', 'normal_contained_in': ['6.a1.c1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.c1', 'projective_image': '24.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701242
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.a1.a1', '12.f1.a1'], 'contains': ['48.b1.a1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 849, -1, 1910, -1, 1293, -1], 'generators': [1, 4], 'label': '144.193.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701243
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.a1.a1', '12.f1.b1'], 'contains': ['48.b1.b1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 1970, -1, 1910, -1, 2204, -1], 'generators': [1, 100], 'label': '144.193.24.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.b1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701244
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.a1.a1', '12.f1.c1'], 'contains': ['48.b1.c1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 3087, -1, 1910, -1, 3409, -1], 'generators': [1, 52], 'label': '144.193.24.b1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.c1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701245
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.d1', '8.a1.b1', '12.f1.a1'], 'contains': ['48.b1.a1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 66, -1, 1910, -1, 1092, -1], 'generators': [6, 4], 'label': '144.193.24.b1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.d1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701246
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.e1', '8.a1.b1', '12.f1.b1'], 'contains': ['48.b1.b1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 1434, -1, 1910, -1, 1688, -1], 'generators': [6, 100], 'label': '144.193.24.b1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.e1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701247
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.f1', '8.a1.b1', '12.f1.c1'], 'contains': ['48.b1.c1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 2331, -1, 1910, -1, 3216, -1], 'generators': [6, 52], 'label': '144.193.24.b1.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.f1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701248
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.g1', '8.a1.c1', '12.f1.a1'], 'contains': ['48.b1.a1', '72.a1.c1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 344, -1, 1910, -1, 1487, -1], 'generators': [7, 4], 'label': '144.193.24.b1.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.g1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701249
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.h1', '8.a1.c1', '12.f1.b1'], 'contains': ['48.b1.b1', '72.a1.c1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 1609, -1, 1910, -1, 2453, -1], 'generators': [7, 100], 'label': '144.193.24.b1.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.h1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701250
    {'ambient': '144.193', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.i1', '8.a1.c1', '12.f1.c1'], 'contains': ['48.b1.c1', '72.a1.c1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [944, -1, 2716, -1, 1910, -1, 3603, -1], 'generators': [7, 52], 'label': '144.193.24.b1.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.i1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701251
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['48.a1.a1', '48.b1.a1', '48.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '6.b1.e1', '6.b1.h1', '9.a1.a1', '12.f1.b1'], 'core': '3.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2490, 6434, 3360, 3111, 2328, 5859, 2690, 4796], 'generators': [1, 72, 6, 100, 12], 'label': '144.193.3.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.b1', '6.b1.h1', '6.b1.e1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.b1', 'projective_image': '36.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701252
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.d1.b1', '12.d1.c1', '12.g1.a1', '12.g1.b1', '12.g1.c1'], 'contains': ['48.a1.a1', '72.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4884, -1, 6708, -1, 5550, -1, 6345, -1], 'generators': [12, 48], 'label': '144.193.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '48.49', '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': '1.1'}
  • id: 11701253
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.b1', '12.e1.c1', '12.g1.a1', '12.h1.a1', '12.h1.a2'], 'contains': ['48.a1.a1', '72.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7531, -1, 9564, -1, 7168, -1, 7927, -1], 'generators': [13, 48], 'label': '144.193.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.49', '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': '1.1'}
  • id: 11701254
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.e1.a1', '12.e1.c1', '12.g1.b1', '12.h1.a1', '12.h1.a2'], 'contains': ['48.a1.a1', '72.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7531, -1, 8830, -1, 7168, -1, 8563, -1], 'generators': [18, 48], 'label': '144.193.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '48.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701255
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.c1', '12.e1.a1', '12.e1.b1', '12.g1.c1', '12.h1.a1', '12.h1.a2'], 'contains': ['48.a1.a1', '72.c1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7531, -1, 9098, -1, 7168, -1, 7645, -1], 'generators': [19, 48], 'label': '144.193.24.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.c1', 'projective_image': '48.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701256
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '1.a1.a1', 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.f1.a1', '12.f1.b1', '12.f1.c1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.a1.b1', '72.a1.c1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2599, 8120, 2477, 2346, 4357, 8346, 4237, 2680], 'generators': [1, 6], 'label': '144.193.36.a1.a1', 'mobius_quo': 2, 'mobius_sub': -12, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['9.a1.a1', '12.a1.a1'], 'normal_contains': ['72.a1.a1', '72.a1.c1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '36.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701257
    {'ambient': '144.193', 'aut_centralizer_order': 144, 'aut_label': '36.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': ['4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.c1.b1', '12.c1.c1', '18.a1.a1', '18.a1.b1', '18.a1.c1'], 'contains': ['72.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4036, 2480, 4334, 4393, 3438, 3739, 3930, 4558], 'generators': [12, 72], 'label': '144.193.36.b1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '12.c1.c1', '12.c1.b1', '18.a1.a1', '18.a1.c1', '18.a1.b1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '144.193', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 11701258
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5780, -1, 5740, -1, 6078, -1, 5064, -1], 'generators': [1, 12], 'label': '144.193.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '72.47', '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': '1.1'}
  • id: 11701259
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '18.a1.b1', '18.b1.b1', '18.c1.a1'], 'contains': ['72.a1.b1', '72.b1.a1', '72.c1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5780, -1, 6141, -1, 6078, -1, 4650, -1], 'generators': [6, 12], 'label': '144.193.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701260
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.c1', '18.a1.c1', '18.b1.c1', '18.c1.a1'], 'contains': ['72.a1.c1', '72.b1.a1', '72.c1.c1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5780, -1, 5941, -1, 6078, -1, 5477, -1], 'generators': [7, 12], 'label': '144.193.36.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.c1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701261
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.c1.b1', '72.c1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6689, -1, 6930, -1, 7696, -1, 6552, -1], 'generators': [1, 18], 'label': '144.193.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '72.47', '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': '1.1'}
  • id: 11701262
    {'ambient': '144.193', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['48.a1.a1', '48.b1.b1', '48.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '6.b1.f1', '6.b1.i1', '9.a1.a1', '12.f1.c1'], 'core': '3.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2490, 6434, 4721, 4936, 2328, 5859, 3815, 3248], 'generators': [1, 72, 6, 52, 12], 'label': '144.193.3.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.c1', '6.b1.i1', '6.b1.f1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.c1', 'projective_image': '36.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701263
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '18.b1.b1', '18.c1.a1'], 'contains': ['72.a1.b1', '72.c1.a1', '72.c1.c1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6689, -1, 8700, -1, 7696, -1, 5918, -1], 'generators': [13, 6], 'label': '144.193.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.d1.b1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701264
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.c1', '18.b1.c1', '18.c1.a1'], 'contains': ['72.a1.c1', '72.c1.a1', '72.c1.b1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6689, -1, 7623, -1, 7696, -1, 6992, -1], 'generators': [13, 18], 'label': '144.193.36.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.d1.c1', 'projective_image': '72.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701265
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.a1.a1', '18.b1.b1', '18.b1.c1'], 'contains': ['72.b1.a1', '72.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': '36T103', 'count': 3, 'diagramx': [7510, -1, 8008, -1, 6640, -1, 6138, -1], 'generators': [73, 12], 'label': '144.193.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '144.193', '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': '1.1'}
  • id: 11701266
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '18.a1.b1', '18.b1.a1', '18.b1.c1'], 'contains': ['72.b1.a1', '72.c1.b1'], 'core': '144.a1.a1', 'coset_action_label': '36T103', 'count': 3, 'diagramx': [7510, -1, 7130, -1, 6640, -1, 6772, -1], 'generators': [78, 12], 'label': '144.193.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.b1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701267
    {'ambient': '144.193', 'aut_centralizer_order': 48, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.c1', '18.a1.c1', '18.b1.a1', '18.b1.b1'], 'contains': ['72.b1.a1', '72.c1.c1'], 'core': '144.a1.a1', 'coset_action_label': '36T103', 'count': 3, 'diagramx': [7510, -1, 7330, -1, 6640, -1, 5698, -1], 'generators': [79, 12], 'label': '144.193.36.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.c1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701268
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1'], 'contains': ['72.c1.a1', '72.c1.b1', '72.c1.c1'], 'core': '144.a1.a1', 'coset_action_label': '36T138', 'count': 3, 'diagramx': [9378, -1, 8301, -1, 8848, -1, 7433, -1], 'generators': [85, 18], 'label': '144.193.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '144.193', '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': '1.1'}
  • id: 11701269
    {'ambient': '144.193', 'aut_centralizer_order': 24, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a2', '18.b1.a1', '18.b1.b1', '18.b1.c1'], 'contains': ['72.c1.a1', '72.c1.b1', '72.c1.c1'], 'core': '144.a1.a1', 'coset_action_label': '36T138', 'count': 3, 'diagramx': [9378, -1, 8501, -1, 8848, -1, 7212, -1], 'generators': [73, 18], 'label': '144.193.36.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a2', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701270
    {'ambient': '144.193', 'aut_centralizer_order': 432, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.a1.c1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1'], 'contains': ['144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3639, 3857, 6420, 1844, 5057, 5055, 5472, 1922], 'generators': [48], 'label': '144.193.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 8, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.b1.a1', '24.a1.a1', '24.a1.c1', '24.a1.b1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.49', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.49', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701271
    {'ambient': '144.193', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.a1.a1', '24.b1.a1', '24.b1.d1', '24.b1.g1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2059, -1, 780, -1, 1649, -1, 1390, -1], 'generators': [4], 'label': '144.193.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '144.193', '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': '1.1'}
  • id: 11701272
    {'ambient': '144.193', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '16.a1.a1', '24.b1.b1', '24.b1.e1', '24.b1.h1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2059, -1, 1851, -1, 1649, -1, 2131, -1], 'generators': [100], 'label': '144.193.48.b1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.b1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701273
    {'ambient': '144.193', 'aut_centralizer_order': 6, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': ['36.a1.a1', '36.d1.b1', '36.d1.a1', '36.d1.c1', '36.f1.a2', '36.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.a1.c1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.c1.b1', '12.c1.c1', '16.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3748, 1492, 2753, 8495, 401, 1069, 1814, 6827], 'generators': [4, 48, 84, 72], 'label': '144.193.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.c1', '2.a1.b1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.c1.c1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '48.49', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 11701274
    {'ambient': '144.193', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.c1', '16.a1.a1', '24.b1.c1', '24.b1.f1', '24.b1.i1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2059, -1, 3041, -1, 1649, -1, 3313, -1], 'generators': [52], 'label': '144.193.48.b1.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.c1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701275
    {'ambient': '144.193', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['2.a1.b1', '2.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.b1.b1', '24.b1.c1', '36.a1.a1', '36.c1.a1', '36.d1.a1'], 'contains': ['144.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3132, 5697, 3494, 3552, 5550, 6609, 4430, 3067], 'generators': [1], 'label': '144.193.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': 12, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.47', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701276
    {'ambient': '144.193', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['2.a1.a1', '2.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.b1.d1', '24.b1.e1', '24.b1.f1', '36.a1.a1', '36.c1.b1', '36.d1.b1'], 'contains': ['144.a1.a1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3132, 5697, 2531, 2931, 5550, 6609, 4237, 2304], 'generators': [6], 'label': '144.193.72.a1.b1', 'mobius_quo': -1, 'mobius_sub': 12, 'normal_closure': '72.a1.b1', 'normal_contained_in': ['18.a1.b1', '24.a1.b1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.b1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.47', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701277
    {'ambient': '144.193', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['2.a1.b1', '2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.c1', '24.b1.g1', '24.b1.h1', '24.b1.i1', '36.a1.a1', '36.c1.c1', '36.d1.c1'], 'contains': ['144.a1.a1'], 'core': '72.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3132, 5697, 2880, 2444, 5550, 6609, 4623, 2686], 'generators': [7], 'label': '144.193.72.a1.c1', 'mobius_quo': -1, 'mobius_sub': 12, 'normal_closure': '72.a1.c1', 'normal_contained_in': ['18.a1.c1', '24.a1.c1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.c1', 'projective_image': '72.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.47', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701278
    {'ambient': '144.193', 'aut_centralizer_order': 288, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1', '36.c1.c1', '36.e1.a1', '36.e1.b1', '36.e1.c1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4965, -1, 6141, -1, 6044, -1, 5279, -1], 'generators': [12], 'label': '144.193.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '144.193', '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': '1.1'}
  • id: 11701279
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.c1.a1', '36.d1.b1', '36.d1.c1', '36.e1.a1', '36.f1.a1', '36.f1.a2'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6928, -1, 8006, -1, 6901, -1, 6412, -1], 'generators': [13], 'label': '144.193.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '144.193', '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': '1.1'}
  • id: 11701280
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '36.c1.b1', '36.d1.a1', '36.d1.c1', '36.e1.b1', '36.f1.a1', '36.f1.a2'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6928, -1, 7398, -1, 6901, -1, 6882, -1], 'generators': [18], 'label': '144.193.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.c1.b1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701281
    {'ambient': '144.193', 'aut_centralizer_order': 96, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.c1', '36.c1.c1', '36.d1.a1', '36.d1.b1', '36.e1.c1', '36.f1.a1', '36.f1.a2'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6928, -1, 8376, -1, 6901, -1, 6205, -1], 'generators': [19], 'label': '144.193.72.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.c1.c1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 11701282
    {'ambient': '144.193', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '72.a1.a1', '72.a1.b1', '72.a1.c1', '72.b1.a1', '72.c1.a1', '72.c1.b1', '72.c1.c1'], 'contains': [], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3639, 3857, 3494, 2931, 5550, 5055, 4623, 2686], 'generators': [], 'label': '144.193.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': -24, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.b1.a1', '48.a1.a1', '72.a1.a1', '72.a1.c1', '72.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '144.193', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}