Abstract group data - 192.967

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• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.5', '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, 2, 2, 3, 2, 2], 'aut_gens': [[10622, 22356, 37001, 38921], [10622, 18869, 38921, 37001], [27482, 22356, 37001, 38921], [27482, 57300, 37001, 38921], [42422, 22356, 37001, 38921], [8702, 22356, 37001, 38921], [7935, 22356, 38921, 6273], [43382, 55260, 37001, 38921], [43382, 57180, 37001, 38921]], 'aut_group': '384.20051', 'aut_hash': 20051, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 10, 'aut_perms': [85806, 1, 120, 414, 126, 80640, 367920, 1174320], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [3, 8, 1, 1], [4, 1, 2, 2], [4, 3, 2, 2], [6, 8, 1, 1], [6, 8, 2, 1], [8, 6, 8, 2], [12, 8, 2, 2]], 'aut_supersolvable': False, 'aut_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', '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, 8, 1], [4, 1, 4], [4, 3, 4], [6, 8, 3], [8, 6, 16], [12, 8, 4]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '12.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 967, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['96.65', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [3, 8, 1, 1], [4, 1, 2, 2], [4, 3, 2, 2], [6, 8, 1, 3], [8, 6, 4, 4], [12, 8, 2, 2]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '48.48', 'hash': 967, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 2], 'inner_gens': [[10622, 18869, 38921, 37001], [55715, 22356, 6273, 37001], [43382, 55260, 37001, 38921], [43382, 57180, 37001, 38921]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 8], [3, 16]], 'label': '192.967', 'linC_count': 96, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 8, 'linQ_dim': 7, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*A4:C8', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 17, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 40, 'number_divisions': 22, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 89, 'number_subgroups': 254, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 8], [4, 16], [6, 24], [8, 96], [12, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [4097, 4097, 4097, 4097], 'outer_gens': [[61202, 22356, 37001, 38921], [10622, 57300, 37001, 38921], [25562, 22356, 37001, 38921], [8702, 22356, 37001, 38921]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [3, 4], [4, 4], [6, 2], [12, 2]], 'representations': {'PC': {'code': 2357542013485511820773904007792004, 'gens': [1, 4, 6, 7], 'pres': [7, -2, -2, -2, -2, -3, -2, 2, 14, 36, 1123, 80, 1124, 4037, 782, 285, 2358, 321, 475]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 160, 8645, 18685, 2665, 9889, 1801]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [36873, 8694, 63503, 51027, 12291, 39049, 4225]}, 'Perm': {'d': 14, 'gens': [479416471, 1, 859248, 1270440, 518918400, 6266937600, 13412044800]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times A_4:C_8', 'transitive_degree': 48, '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: 172731983
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 967, 'group_order': 192, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 4097, 'size': 1}
  • id: 172731994
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 967, 'group_order': 192, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 36873, 'size': 1}
  • id: 172732005
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 967, 'group_order': 192, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 28679, 'size': 1}
  • id: 172732016
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 967, 'group_order': 192, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 61455, 'size': 1}
  • id: 172732018
    {'aut_label': '2D', 'centralizer': '3.a1.a1', 'counter': 5, 'group_counter': 967, 'group_order': 192, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 38921, 'size': 3}
  • id: 172732019
    {'aut_label': '2E', 'centralizer': '3.a1.a1', 'counter': 6, 'group_counter': 967, 'group_order': 192, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 6145, 'size': 3}
  • id: 172732020
    {'aut_label': '2F', 'centralizer': '3.a1.a1', 'counter': 7, 'group_counter': 967, 'group_order': 192, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 63503, 'size': 3}
  • id: 172732021
    {'aut_label': '2F', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 967, 'group_order': 192, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 30727, 'size': 3}
  • id: 172732022
    {'aut_label': '3A', 'centralizer': '8.c1.a1', 'counter': 9, 'group_counter': 967, 'group_order': 192, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 53203, 'size': 8}
  • id: 172731984
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 967, 'group_order': 192, 'label': '4A1', 'order': 4, 'powers': [2, 11], 'representative': 12291, 'size': 1}
  • id: 172731985
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 967, 'group_order': 192, 'label': '4A-1', 'order': 4, 'powers': [2, 10], 'representative': 45067, 'size': 1}
  • id: 172731986
    {'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 967, 'group_order': 192, 'label': '4B1', 'order': 4, 'powers': [2, 13], 'representative': 53261, 'size': 1}
  • id: 172731987
    {'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 967, 'group_order': 192, 'label': '4B-1', 'order': 4, 'powers': [2, 12], 'representative': 20485, 'size': 1}
  • id: 172731988
    {'aut_label': '4C1', 'centralizer': '3.a1.a1', 'counter': 14, 'group_counter': 967, 'group_order': 192, 'label': '4C1', 'order': 4, 'powers': [2, 15], 'representative': 55309, 'size': 3}
  • id: 172731989
    {'aut_label': '4C1', 'centralizer': '3.a1.a1', 'counter': 15, 'group_counter': 967, 'group_order': 192, 'label': '4C-1', 'order': 4, 'powers': [2, 14], 'representative': 22533, 'size': 3}
  • id: 172731990
    {'aut_label': '4D1', 'centralizer': '3.a1.a1', 'counter': 16, 'group_counter': 967, 'group_order': 192, 'label': '4D1', 'order': 4, 'powers': [2, 17], 'representative': 14467, 'size': 3}
  • id: 172731991
    {'aut_label': '4D1', 'centralizer': '3.a1.a1', 'counter': 17, 'group_counter': 967, 'group_order': 192, 'label': '4D-1', 'order': 4, 'powers': [2, 16], 'representative': 47243, 'size': 3}
  • id: 172731992
    {'aut_label': '6A', 'centralizer': '8.c1.a1', 'counter': 18, 'group_counter': 967, 'group_order': 192, 'label': '6A', 'order': 6, 'powers': [9, 3], 'representative': 22356, 'size': 8}
  • id: 172731993
    {'aut_label': '6A', 'centralizer': '8.c1.a1', 'counter': 19, 'group_counter': 967, 'group_order': 192, 'label': '6B', 'order': 6, 'powers': [9, 4], 'representative': 57300, 'size': 8}
  • id: 172731995
    {'aut_label': '6C', 'centralizer': '8.c1.a1', 'counter': 20, 'group_counter': 967, 'group_order': 192, 'label': '6C', 'order': 6, 'powers': [9, 2], 'representative': 47548, 'size': 8}
  • id: 172731996
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 21, 'group_counter': 967, 'group_order': 192, 'label': '8A1', 'order': 8, 'powers': [10, 23], 'representative': 10622, 'size': 6}
  • id: 172731997
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 967, 'group_order': 192, 'label': '8A-1', 'order': 8, 'powers': [11, 24], 'representative': 25562, 'size': 6}
  • id: 172731998
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 967, 'group_order': 192, 'label': '8A3', 'order': 8, 'powers': [11, 21], 'representative': 27482, 'size': 6}
  • id: 172731999
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 24, 'group_counter': 967, 'group_order': 192, 'label': '8A-3', 'order': 8, 'powers': [10, 22], 'representative': 8702, 'size': 6}
  • id: 172732000
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 25, 'group_counter': 967, 'group_order': 192, 'label': '8B1', 'order': 8, 'powers': [16, 27], 'representative': 8694, 'size': 6}
  • id: 172732001
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 26, 'group_counter': 967, 'group_order': 192, 'label': '8B-1', 'order': 8, 'powers': [17, 28], 'representative': 27474, 'size': 6}
  • id: 172732002
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 27, 'group_counter': 967, 'group_order': 192, 'label': '8B3', 'order': 8, 'powers': [17, 25], 'representative': 25554, 'size': 6}
  • id: 172732003
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 28, 'group_counter': 967, 'group_order': 192, 'label': '8B-3', 'order': 8, 'powers': [16, 26], 'representative': 10614, 'size': 6}
  • id: 172732004
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 29, 'group_counter': 967, 'group_order': 192, 'label': '8C1', 'order': 8, 'powers': [10, 31], 'representative': 29337, 'size': 6}
  • id: 172732006
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 30, 'group_counter': 967, 'group_order': 192, 'label': '8C-1', 'order': 8, 'powers': [11, 32], 'representative': 54835, 'size': 6}
  • id: 172732007
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 31, 'group_counter': 967, 'group_order': 192, 'label': '8C3', 'order': 8, 'powers': [11, 29], 'representative': 22203, 'size': 6}
  • id: 172732008
    {'aut_label': '8A1', 'centralizer': '6.b1.a1', 'counter': 32, 'group_counter': 967, 'group_order': 192, 'label': '8C-3', 'order': 8, 'powers': [10, 30], 'representative': 61969, 'size': 6}
  • id: 172732009
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 33, 'group_counter': 967, 'group_order': 192, 'label': '8D1', 'order': 8, 'powers': [16, 35], 'representative': 64025, 'size': 6}
  • id: 172732010
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 34, 'group_counter': 967, 'group_order': 192, 'label': '8D-1', 'order': 8, 'powers': [17, 36], 'representative': 24243, 'size': 6}
  • id: 172732011
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 35, 'group_counter': 967, 'group_order': 192, 'label': '8D3', 'order': 8, 'powers': [17, 33], 'representative': 56891, 'size': 6}
  • id: 172732012
    {'aut_label': '8B1', 'centralizer': '6.c1.a1', 'counter': 36, 'group_counter': 967, 'group_order': 192, 'label': '8D-3', 'order': 8, 'powers': [16, 34], 'representative': 31377, 'size': 6}
  • id: 172732013
    {'aut_label': '12A1', 'centralizer': '8.c1.a1', 'counter': 37, 'group_counter': 967, 'group_order': 192, 'label': '12A1', 'order': 12, 'powers': [20, 11], 'representative': 19833, 'size': 8}
  • id: 172732014
    {'aut_label': '12A1', 'centralizer': '8.c1.a1', 'counter': 38, 'group_counter': 967, 'group_order': 192, 'label': '12A-1', 'order': 12, 'powers': [20, 10], 'representative': 17905, 'size': 8}
  • id: 172732015
    {'aut_label': '12B1', 'centralizer': '8.c1.a1', 'counter': 39, 'group_counter': 967, 'group_order': 192, 'label': '12B1', 'order': 12, 'powers': [20, 12], 'representative': 62972, 'size': 8}
  • id: 172732017
    {'aut_label': '12B1', 'centralizer': '8.c1.a1', 'counter': 40, 'group_counter': 967, 'group_order': 192, 'label': '12B-1', 'order': 12, 'powers': [20, 13], 'representative': 32124, 'size': 8}
• 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: 17547247
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17547258
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 17547262
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 17547263
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17547264
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2], 'schur_index': 1}
  • id: 17547265
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
  • id: 17547268
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17547248
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, -2, -2, -1, 2, -2, -2, 2, 2, 2, -2, -2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 17547249
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2c', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, -2, -2, -1, -2, 2, 2, -2, -2, -2, 2, 2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1], 'schur_index': 2}
  • id: 17547250
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2d', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 2}
  • id: 17547253
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547254
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547255
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -1, -1, 1, 1, 0, 3, -3, -3, 3, -1, -1, 1, 1, 0, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547256
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -1, -1, 1, 1, 0, 3, -3, -3, 3, -1, -1, 1, 1, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547266
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1g', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547267
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.1h', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547251
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2e', 'multiplicity': 2, 'nt': [24, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547252
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.2f', 'multiplicity': 2, 'nt': [24, 8], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547257
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3e', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -2, -2, 2, 2, 0, -6, 6, 6, -6, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547259
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3f', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, 0, -6, -6, -6, -6, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547260
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3g', 'multiplicity': 4, 'nt': [24, 89], 'qdim': 12, 'qvalues': [12, -12, 12, -12, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17547261
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '192.967', 'group_order': 192, 'image': None, 'label': '192.967.3h', 'multiplicity': 4, 'nt': [24, 89], 'qdim': 12, 'qvalues': [12, 12, -12, -12, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 38300939
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 192, 'label': '192.967.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300950
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 96, 'label': '192.967.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300961
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 96, 'label': '192.967.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300972
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 96, 'label': '192.967.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300974
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 48, 'label': '192.967.1e1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 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, 0]]]}
  • id: 38300975
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 48, 'label': '192.967.1e2', 'nt': [4, 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, 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, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38300976
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 48, 'label': '192.967.1f1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 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, 0]]]}
  • id: 38300977
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 48, 'label': '192.967.1f2', 'nt': [4, 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, 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, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38300978
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 24, 'label': '192.967.1g1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 38300940
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 24, 'label': '192.967.1g2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 38300941
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 11, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 24, 'label': '192.967.1g3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 38300942
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 12, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 24, 'label': '192.967.1g4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 38300943
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.967.1h1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 38300944
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 14, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.967.1h2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 38300945
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 15, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.967.1h3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 38300946
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 16, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.967.1h4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 38300947
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 32, 'label': '192.967.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38300948
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 16, 'label': '192.967.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38300949
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.a1', 'kernel_order': 16, 'label': '192.967.2c', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300951
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 16, 'label': '192.967.2d', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38300952
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.b1', 'kernel_order': 8, 'label': '192.967.2e1', 'nt': [24, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[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]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 38300953
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.b1', 'kernel_order': 8, 'label': '192.967.2e2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[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]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 38300954
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 8, 'label': '192.967.2f1', 'nt': [24, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-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]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 38300955
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.1', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 8, 'label': '192.967.2f2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-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]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 38300956
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 8, 'label': '192.967.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300957
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 8, 'label': '192.967.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300958
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.967.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300959
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.967.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300960
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.c1.a1', 'kernel_order': 4, 'label': '192.967.3e1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300962
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.c1.a1', 'kernel_order': 4, 'label': '192.967.3e2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300963
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 4, 'label': '192.967.3f1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300964
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 4, 'label': '192.967.3f2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300965
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 2, 'label': '192.967.3g1', 'nt': [24, 89], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 2]], [[-3, 2]], [[3, 2]], [[3, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300966
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 2, 'label': '192.967.3g2', 'nt': [24, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 2]], [[3, 2]], [[-3, 2]], [[-3, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300967
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 2, 'label': '192.967.3g3', 'nt': [24, 89], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 2]], [[-3, 2]], [[3, 2]], [[3, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300968
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 2, 'label': '192.967.3g4', 'nt': [24, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 2]], [[3, 2]], [[-3, 2]], [[-3, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300969
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 2, 'label': '192.967.3h1', 'nt': [24, 89], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 2]], [[3, 2]], [[-3, 2]], [[3, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300970
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 2, 'label': '192.967.3h2', 'nt': [24, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 2]], [[-3, 2]], [[3, 2]], [[-3, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300971
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 39, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 2, 'label': '192.967.3h3', 'nt': [24, 89], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 2]], [[3, 2]], [[-3, 2]], [[3, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38300973
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 40, 'cyclotomic_n': 8, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.967', 'group_counter': 967, 'group_order': 192, 'image': None, 'image_isoclass': '96.65', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 2, 'label': '192.967.3h4', 'nt': [24, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 2]], [[-3, 2]], [[3, 2]], [[-3, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[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: 264590770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '192.967.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.967', 'subgroup_hash': 967, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 264590781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264590792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '192.967.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 264590803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '192.967.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.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': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 264590814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '192.967.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.87', 'subgroup_hash': 87, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 2}
  • id: 264590825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 264590836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264590847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264590858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.4.d1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 24, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264590779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', '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: 264590780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', '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: 264590782
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264590783
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590784
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 264590786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590799
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 12, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], '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: 264590802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264590804
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264590805
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264590806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.24.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': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590807
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264590808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_8', '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: 264590809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_8', '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: 264590810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264590811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264590813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590821
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590824
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 264590826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264590827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264590828
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264590829
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264590830
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264590831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590832
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 66, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.967.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590833
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 67, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.967.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.967.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_8', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], '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: 264590835
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590838
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264590840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 264590842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 264590844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.967.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264590849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '192.967.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 264590850
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 2, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.967.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.194', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 194, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2.S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264590851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '192.967.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.65', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 65, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_8', '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: 264590852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '192.967.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.65', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 65, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_8', '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: 264590853
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 264590854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 264590855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 264590856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.967.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, '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: 264590857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.967', 'ambient_counter': 967, 'ambient_order': 192, 'ambient_tex': 'C_2\\times A_4:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 1, 'counter': 89, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '192.967.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '192.967', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 967, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4:C_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C6'], '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: 264590770
    {'ambient': '192.967', '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': '24.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '4.d1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7129, 6324, 6417, 8094, 6480, 5508, 3263, 1780], 'generators': [10622, 6273, 53203, 28679, 38921, 12291, 36873], 'label': '192.967.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '24.12', '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': '24.12'}
  • id: 264590771
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 16, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.h1.a1', '12.i1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4641, 9067, 4974, 7749, 4333, 8929, 5949, 2995], 'generators': [12291, 28679, 37001, 38921], 'label': '192.967.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '24.12', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590772
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 12, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.j1.a1', '12.j1.b1', '12.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8857, -1, 8966, -1, 7133, -1, 1898, -1], 'generators': [10622, 28679, 6273], 'label': '192.967.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '24.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590773
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 12, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.g1.a1', '12.k1.a1', '12.k1.b1', '12.m1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7156, -1, 6936, -1, 8706, -1, 3248, -1], 'generators': [8694, 28679, 6273], 'label': '192.967.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '24.12', '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': '2.1'}
  • id: 264590774
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 12, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.h1.a1', '12.j1.a1', '12.k1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8253, -1, 7716, -1, 8127, -1, 3671, -1], 'generators': [10622, 63503], 'label': '192.967.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '48.48', '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': '4.2'}
  • id: 264590775
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 12, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.h1.a1', '12.j1.b1', '12.k1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8253, -1, 8072, -1, 8127, -1, 2470, -1], 'generators': [8694, 63503], 'label': '192.967.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264590776
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 24, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.j1.a1', '12.k1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7821, -1, 8427, -1, 7661, -1, 2824, -1], 'generators': [10622, 38921], 'label': '192.967.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264590777
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 24, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.j1.b1', '12.k1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7821, -1, 7361, -1, 7661, -1, 4026, -1], 'generators': [29337, 38921], 'label': '192.967.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264590778
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '32.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1602, 3086, 2236, 4190, 1271, 2982, 7885, 5000], 'generators': [36873, 53203, 37001, 38921], 'label': '192.967.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590779
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': ['24.n1.a1', '24.o1.a1', '24.n1.b1', '24.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '32.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [398, 933, 1133, 2468, 258, 901, 8855, 9289], 'generators': [28679, 53203, 37001, 38921], 'label': '192.967.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '96.65', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590780
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': ['24.n1.a1', '24.o1.a1', '24.n1.b1', '24.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.c1.b1', '32.b1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [398, 933, 654, 746, 258, 901, 8431, 7649], 'generators': [61455, 53203, 37001, 38921], 'label': '192.967.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '96.65', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590781
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1', '8.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3268, 7519, 4139, 6167, 2538, 6679, 5676, 3615], 'generators': [12291, 38921, 37001, 28679, 53203, 36873], 'label': '192.967.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '24.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590782
    {'ambient': '192.967', 'aut_centralizer_order': 12, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.d1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '24.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2925, -1, 3989, -1, 2327, -1, 4339, -1], 'generators': [12291, 28679, 53203, 36873], 'label': '192.967.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.c1.a1', 'projective_image': '24.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590783
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.d1.a1'], 'contains': ['16.c1.a1', '24.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6461, -1, 6310, -1, 6664, -1, 832, -1], 'generators': [10622, 12291, 36873, 53203], 'label': '192.967.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.d1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590784
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '4.d1.a1'], 'contains': ['16.c1.a1', '24.n1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6461, -1, 6014, -1, 6664, -1, 116, -1], 'generators': [29337, 12291, 36873, 53203], 'label': '192.967.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.d1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590785
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 32, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.f1.a1', '24.p1.a1', '24.p1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2038, 4378, 2322, 4969, 1697, 4661, 9197, 6324], 'generators': [36873, 28679, 37001, 38921], 'label': '192.967.12.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.c1.b1', '24.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '48.30', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590786
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 32, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.j1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5390, 6291, 4614, 8999, 3719, 6510, 5949, 844], 'generators': [12291, 37001, 38921], 'label': '192.967.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '48.48', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590787
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 32, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.h1.a1', '24.i1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2967, 8795, 3265, 6499, 3105, 8929, 7427, 3226], 'generators': [53261, 37001, 38921], 'label': '192.967.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '48.30', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590788
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '24.g1.a1', '24.h1.a1', '24.k1.a1', '24.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6590, -1, 5845, -1, 6175, -1, 4964, -1], 'generators': [12291, 28679, 37001], 'label': '192.967.12.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': '24.12', '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: 264590789
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.i1.a1', '24.j1.a1', '24.m1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4041, -1, 5351, -1, 4947, -1, 6934, -1], 'generators': [47115, 28679, 37001], 'label': '192.967.12.e1.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.e1.a1', 'projective_image': '48.30', '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': '2.1'}
  • id: 264590790
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.n1.a1', '24.n1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8857, -1, 9915, -1, 7110, -1, 474, -1], 'generators': [10622, 28679], 'label': '192.967.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '24.12', '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: 264590791
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.e1.a1', '24.o1.a1', '24.o1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7152, -1, 7229, -1, 9769, -1, 3323, -1], 'generators': [8694, 28679], 'label': '192.967.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.30', '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: 264590792
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': ['96.b1.a1', '96.e1.a1', '96.b1.b1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '6.e1.a1', '8.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 5111, 6621, 8094, 6629, 4353, 2824, 674], 'generators': [10622, 38921, 6273, 12291, 36873, 53203], 'label': '192.967.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '48.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590793
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.i1.a1', '24.k1.a1', '24.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5990, -1, 6338, -1, 5561, -1, 5457, -1], 'generators': [12291, 63503, 37001], 'label': '192.967.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '48.48', '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': '2.1'}
  • id: 264590794
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.f1.a1', '24.h1.a1', '24.j1.a1', '24.l1.a1', '24.m1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4641, -1, 3759, -1, 4333, -1, 6442, -1], 'generators': [47115, 63503, 37001], 'label': '192.967.12.i1.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.i1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590795
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.g1.a1', '24.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9377, -1, 9060, -1, 8174, -1, 2043, -1], 'generators': [10622, 6273], 'label': '192.967.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590796
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.g1.a1', '24.n1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9377, -1, 8632, -1, 8174, -1, 1616, -1], 'generators': [29337, 37001], 'label': '192.967.12.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590797
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.g1.a1', '24.o1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8338, -1, 8204, -1, 8706, -1, 2470, -1], 'generators': [8694, 6273], 'label': '192.967.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590798
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 48, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.e1.b1'], 'contains': ['24.g1.a1', '24.o1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8338, -1, 7777, -1, 8706, -1, 3750, -1], 'generators': [64025, 37001], 'label': '192.967.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590799
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.k1.a1', '24.n1.a1', '24.n1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9896, -1, 9487, -1, 7642, -1, 1189, -1], 'generators': [10622, 30855], 'label': '192.967.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590800
    {'ambient': '192.967', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 24, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.l1.a1', '24.o1.a1', '24.o1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7672, -1, 6801, -1, 9237, -1, 2896, -1], 'generators': [8694, 30855], 'label': '192.967.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.m1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590801
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': ['12.f1.a1', '12.g1.a1', '12.l1.a1', '12.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['48.d1.a1', '64.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [313, 1331, 617, 2175, 106, 2550, 8855, 7260], 'generators': [53203, 37001, 38921], 'label': '192.967.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1', '8.b1.b1', '8.a1.a1'], 'normal_contains': ['48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '192.967', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590802
    {'ambient': '192.967', 'aut_centralizer_order': 24, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.c1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1269, -1, 1620, -1, 1154, -1, 7091, -1], 'generators': [36873, 28679, 53203], 'label': '192.967.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.b1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590803
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': ['96.b1.a1', '96.e1.a1', '96.b1.b1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '6.e1.b1', '8.d1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 5111, 6014, 9254, 6629, 4353, 3866, 1780], 'generators': [29337, 38921, 37001, 12291, 36873, 53203], 'label': '192.967.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '48.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590804
    {'ambient': '192.967', 'aut_centralizer_order': 24, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.a1.a1', '48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3341, -1, 4691, -1, 3046, -1, 2931, -1], 'generators': [12291, 53203, 36873], 'label': '192.967.16.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.c1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590805
    {'ambient': '192.967', 'aut_centralizer_order': 24, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.c1.a1'], 'contains': ['32.a1.a1', '48.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2714, -1, 2947, -1, 2702, -1, 4060, -1], 'generators': [53261, 53203, 36873], 'label': '192.967.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.d1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590806
    {'ambient': '192.967', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7447, 8412, 6380, 7736, 5080, 7851, 3282, 2606], 'generators': [12291, 28679], 'label': '192.967.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.12', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590807
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 64, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.k1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2183, 4250, 3022, 4892, 1729, 5585, 8613, 4830], 'generators': [36873, 37001, 38921], 'label': '192.967.24.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.d1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '96.194', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590808
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 64, 'centralizer': '6.a1.a1', 'complements': ['8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.d1.a1', '48.i1.a1', '48.l1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [688, 2814, 607, 3846, 407, 3737, 9868, 8195], 'generators': [28679, 37001, 38921], 'label': '192.967.24.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.d1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '96.65', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590809
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 64, 'centralizer': '6.a1.a1', 'complements': ['8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.a1.a1'], 'contains': ['48.d1.a1', '48.i1.b1', '48.l1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [688, 2814, 865, 2315, 407, 3737, 9611, 6324], 'generators': [61455, 37001, 38921], 'label': '192.967.24.c1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.b1.b1', '12.a1.a1'], 'normal_contains': ['48.d1.a1', '96.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '96.65', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590810
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '48.f1.a1', '48.i1.a1', '48.i1.b1', '48.j1.a1', '48.j1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2787, -1, 3658, -1, 2370, -1, 8098, -1], 'generators': [36873, 28679, 37001], 'label': '192.967.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.30', '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: 264590811
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5887, -1, 6807, -1, 7739, -1, 5265, -1], 'generators': [45195, 28679], 'label': '192.967.24.e1.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.e1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590812
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.l1.a1', '48.l1.b1', '48.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3100, -1, 3401, -1, 2049, -1, 8356, -1], 'generators': [36873, 63503, 37001], 'label': '192.967.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590813
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.h1.a1', '12.j1.a1', '12.j1.b1', '12.k1.a1', '12.k1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7966, -1, 8235, -1, 6676, -1, 3709, -1], 'generators': [12291, 37001], 'label': '192.967.24.g1.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.g1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590814
    {'ambient': '192.967', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 6, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7718, -1, 7481, -1, 7188, -1, 3263, -1], 'generators': [10622, 28679, 38921], 'label': '192.967.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '24.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264590815
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.i1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4182, -1, 4240, -1, 3485, -1, 5692, -1], 'generators': [53261, 37001], 'label': '192.967.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590816
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.h1.a1'], 'contains': ['48.e1.a1', '48.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3662, -1, 4668, -1, 4548, -1, 7518, -1], 'generators': [22533, 37001], 'label': '192.967.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590817
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.i1.a1'], 'contains': ['48.e1.a1', '48.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5367, -1, 5096, -1, 4016, -1, 6545, -1], 'generators': [47115, 37001], 'label': '192.967.24.j1.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.j1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590818
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.h1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6926, -1, 7355, -1, 6144, -1, 4412, -1], 'generators': [12291, 61583], 'label': '192.967.24.k1.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.k1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590819
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.i1.a1', '12.m1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6407, -1, 5524, -1, 7208, -1, 4838, -1], 'generators': [45195, 61583], 'label': '192.967.24.l1.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.l1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590820
    {'ambient': '192.967', 'aut_centralizer_order': 16, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4702, -1, 5952, -1, 5612, -1, 6119, -1], 'generators': [45195, 63503], 'label': '192.967.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590821
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.f1.a1', '12.j1.a1', '12.l1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8857, -1, 9487, -1, 8146, -1, 1302, -1], 'generators': [10622], 'label': '192.967.24.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590822
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.f1.a1', '12.j1.b1', '12.l1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8857, -1, 8632, -1, 8146, -1, 1076, -1], 'generators': [29337], 'label': '192.967.24.n1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.b1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590823
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.k1.a1', '12.m1.a1'], 'contains': ['48.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8364, -1, 7908, -1, 8971, -1, 2454, -1], 'generators': [8694], 'label': '192.967.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.o1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590824
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.k1.b1', '12.m1.a1'], 'contains': ['48.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8364, -1, 7682, -1, 8971, -1, 2680, -1], 'generators': [64025], 'label': '192.967.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.o1.b1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590844
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.p1.a1', '24.p1.b1'], 'contains': ['96.c1.a1', '96.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1911, -1, 2623, -1, 1584, -1, 8870, -1], 'generators': [6145, 37001], 'label': '192.967.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590825
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.a1.a1', '16.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1602, 3037, 1900, 4152, 1271, 2350, 8293, 6543], 'generators': [36873, 38921, 28679, 53203, 37001], 'label': '192.967.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.b1.b1', '8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590826
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.b1', '48.m1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1040, -1, 2444, -1, 727, -1, 9354, -1], 'generators': [6145, 28679, 37001], 'label': '192.967.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.a1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590827
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.i1.b1', '48.j1.b1', '48.k1.a1', '48.l1.a1', '48.m1.a1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1040, -1, 1595, -1, 727, -1, 9096, -1], 'generators': [6145, 63503, 37001], 'label': '192.967.24.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.b1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590828
    {'ambient': '192.967', 'aut_centralizer_order': 48, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1'], 'contains': ['64.a1.a1', '96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1832, -1, 1972, -1, 2526, -1, 5893, -1], 'generators': [36873, 53203], 'label': '192.967.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590829
    {'ambient': '192.967', 'aut_centralizer_order': 24, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.b1.a1'], 'contains': ['64.a1.a1', '96.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [104, -1, 1148, -1, 321, -1, 6966, -1], 'generators': [28679, 53203], 'label': '192.967.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.b1.a1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590830
    {'ambient': '192.967', 'aut_centralizer_order': 24, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '16.b1.a1'], 'contains': ['64.a1.a1', '96.b1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [104, -1, 85, -1, 321, -1, 6740, -1], 'generators': [61455, 53203], 'label': '192.967.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.b1.b1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590831
    {'ambient': '192.967', 'aut_centralizer_order': 192, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.b1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3899, 5334, 4895, 5262, 3148, 4846, 6498, 5595], 'generators': [36873, 28679], 'label': '192.967.48.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1', '96.b1.b1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.30', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590832
    {'ambient': '192.967', 'aut_centralizer_order': 192, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.g1.a1', '24.k1.a1', '24.n1.a1', '24.n1.b1'], 'contains': ['96.a1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7191, 7025, 7764, 7736, 5612, 6618, 3282, 2606], 'generators': [12291], 'label': '192.967.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '48.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.48', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590833
    {'ambient': '192.967', 'aut_centralizer_order': 192, 'aut_label': '48.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.a1.a1', '24.h1.a1', '24.l1.a1'], 'contains': ['96.a1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4786, 8412, 5137, 6729, 3770, 7851, 4838, 3663], 'generators': [53261], 'label': '192.967.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.c1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '48.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.30', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590834
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 64, 'centralizer': '6.a1.a1', 'complements': ['4.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1'], 'contains': ['96.c1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [799, 2814, 740, 3552, 622, 2997, 9899, 7150], 'generators': [37001, 38921], 'label': '192.967.48.d1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.a1.a1', '24.c1.a1', '24.c1.b1', '24.b1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '192.967', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264590835
    {'ambient': '192.967', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.d1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3486, -1, 4379, -1, 2828, -1, 7465, -1], 'generators': [36873, 37001], 'label': '192.967.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590836
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '12.b1.a1', '16.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3601, 5367, 4640, 8234, 2722, 4599, 4892, 1221], 'generators': [12291, 38921, 53203, 36873, 37001], 'label': '192.967.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '48.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590837
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.f1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.e1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4212, -1, 4636, -1, 3469, -1, 7207, -1], 'generators': [36873, 61583], 'label': '192.967.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590838
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '24.m1.a1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4511, -1, 6091, -1, 4673, -1, 6119, -1], 'generators': [20613], 'label': '192.967.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.g1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590839
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.g1.a1', '24.j1.a1', '24.l1.a1', '24.m1.a1', '24.o1.a1', '24.o1.b1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5818, -1, 7166, -1, 6676, -1, 5165, -1], 'generators': [45195], 'label': '192.967.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '96.194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590840
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.p1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.e1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1258, -1, 2246, -1, 1263, -1, 9128, -1], 'generators': [28679, 37001], 'label': '192.967.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590841
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '24.d1.a1', '24.p1.b1'], 'contains': ['96.b1.b1', '96.c1.a1', '96.e1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1258, -1, 1507, -1, 1263, -1, 8613, -1], 'generators': [61455, 37001], 'label': '192.967.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.b1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590842
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.p1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.e1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2236, -1, 3778, -1, 1905, -1, 8098, -1], 'generators': [4225, 28679], 'label': '192.967.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590843
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.p1.b1'], 'contains': ['96.b1.b1', '96.d1.a1', '96.e1.a1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2236, -1, 2882, -1, 1905, -1, 7841, -1], 'generators': [4225, 61583], 'label': '192.967.48.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.b1', 'projective_image': '96.65', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590845
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.a1', '24.p1.b1'], 'contains': ['96.c1.a1', '96.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1571, -1, 1248, -1, 943, -1, 9385, -1], 'generators': [63503, 37001], 'label': '192.967.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590846
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '24.f1.a1', '24.p1.a1'], 'contains': ['96.c1.a1', '96.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1571, -1, 1988, -1, 943, -1, 9642, -1], 'generators': [30727, 37001], 'label': '192.967.48.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.b1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590847
    {'ambient': '192.967', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '16.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2465, 7519, 3051, 6014, 1971, 6679, 6919, 4769], 'generators': [53261, 38921, 53203, 36873, 37001], 'label': '192.967.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '48.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264590848
    {'ambient': '192.967', 'aut_centralizer_order': 32, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.p1.a1', '24.p1.b1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2745, -1, 3139, -1, 2225, -1, 8356, -1], 'generators': [4225, 63503], 'label': '192.967.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.m1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590849
    {'ambient': '192.967', 'aut_centralizer_order': 48, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.a1.a1', '32.b1.a1', '32.b1.b1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [386, -1, 377, -1, 634, -1, 6966, -1], 'generators': [53203], 'label': '192.967.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264590850
    {'ambient': '192.967', 'aut_centralizer_order': 384, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1'], 'contains': ['192.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4212, 5334, 4895, 6090, 3469, 5770, 6119, 4732], 'generators': [36873], 'label': '192.967.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.194', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.194', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590851
    {'ambient': '192.967', 'aut_centralizer_order': 192, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.i1.a1', '48.j1.a1'], 'contains': ['192.a1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1801, 4058, 3419, 5172, 1603, 4291, 7775, 6482], 'generators': [28679], 'label': '192.967.96.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['24.c1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '96.65', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.65', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590852
    {'ambient': '192.967', 'aut_centralizer_order': 192, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '48.a1.a1', '48.i1.b1', '48.j1.b1'], 'contains': ['192.a1.a1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1801, 4058, 2224, 4254, 1603, 4291, 7549, 5607], 'generators': [61455], 'label': '192.967.96.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.b1.b1', 'normal_contained_in': ['24.c1.b1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.b1', 'projective_image': '96.65', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.65', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590853
    {'ambient': '192.967', 'aut_centralizer_order': 128, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.e1.a1', '48.i1.a1', '48.i1.b1', '48.k1.a1', '48.l1.a1', '48.l1.b1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1219, -1, 1627, -1, 1283, -1, 8999, -1], 'generators': [37001], 'label': '192.967.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590854
    {'ambient': '192.967', 'aut_centralizer_order': 128, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.j1.a1', '48.j1.b1', '48.k1.a1', '48.m1.a1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2527, -1, 3778, -1, 2167, -1, 8001, -1], 'generators': [4225], 'label': '192.967.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.d1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590855
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.i1.a1', '48.j1.b1', '48.l1.a1', '48.m1.a1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2156, -1, 2583, -1, 1885, -1, 8227, -1], 'generators': [61583], 'label': '192.967.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.e1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590856
    {'ambient': '192.967', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 384, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.i1.b1', '48.j1.a1', '48.l1.b1', '48.m1.a1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2156, -1, 2935, -1, 1885, -1, 8453, -1], 'generators': [28807], 'label': '192.967.96.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.e1.b1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590857
    {'ambient': '192.967', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.b1.b1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.e1.b1'], 'contains': [], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1938, 4058, 2821, 4713, 1744, 4291, 7888, 6045], 'generators': [], 'label': '192.967.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.d1.a1', '96.b1.a1', '96.b1.b1', '96.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.967', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264590858
    {'ambient': '192.967', 'aut_centralizer_order': 1, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 4, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.d1.b1', '12.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6717, -1, 6257, -1, 6296, -1, 832, -1], 'generators': [10622, 53203, 28679, 12291, 36873], 'label': '192.967.4.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '4.d1.a1', 'projective_image': '24.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}