Abstract group data - 96.170

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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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 4], 'aut_gens': [[1, 6, 24], [49, 6, 24], [1, 54, 24], [5, 6, 24], [13, 54, 24], [1, 6, 36], [13, 54, 84], [13, 9, 75]], 'aut_group': '256.29598', 'aut_hash': 29598, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 256, 'aut_permdeg': 14, 'aut_perms': [12933407640, 12933043200, 13412407680, 13412046365, 11536, 11520, 18681441967], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 4, 1, 1], [3, 1, 2, 1], [4, 2, 4, 1], [4, 4, 1, 1], [4, 4, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 4, 1], [6, 4, 2, 1], [12, 2, 8, 1], [12, 4, 2, 1], [12, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 1], [3, 1, 2], [4, 2, 4], [4, 4, 3], [6, 1, 6], [6, 2, 4], [6, 4, 2], [12, 2, 8], [12, 4, 6]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 170, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['32.30', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 1], [3, 1, 2, 1], [4, 2, 2, 2], [4, 4, 1, 3], [6, 1, 2, 3], [6, 2, 2, 2], [6, 4, 2, 1], [12, 2, 4, 2], [12, 4, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1092, 'exponent': 12, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '24.15', 'hash': 170, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 6, 36], [1, 6, 72], [13, 54, 24]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 18]], 'label': '96.170', 'linC_count': 96, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 36, 'linQ_dim': 8, 'linQ_dim_count': 36, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2^2*C12):C2', 'ngens': 6, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 16, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 42, 'number_divisions': 24, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 78, 'number_subgroups': 116, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 11], [3, 2], [4, 20], [6, 22], [12, 40]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 91, 0], 'outer_gens': [[5, 18, 24], [53, 54, 24], [53, 9, 75], [65, 9, 27]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [23, 16, 5183, 15127], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [8, 2]], 'representations': {'PC': {'code': 5938008110941520, 'gens': [1, 3, 5], 'pres': [6, -2, -3, -2, -2, 2, -2, 12, 50, 1084, 376, 88]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083311105, 1087522049, 1087751937, 2149582850, 1087570945, 2180074818]}, 'Perm': {'d': 15, 'gens': [87665276424, 199395302400, 275992053864, 4, 382403669760, 1680]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times C_{12}):C_2', '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: 105870993
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 170, 'group_order': 96, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 105871004
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 170, 'group_order': 96, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 12, 'size': 1}
  • id: 105871015
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 170, 'group_order': 96, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 48, 'size': 1}
  • id: 105871026
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 170, 'group_order': 96, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 60, 'size': 1}
  • id: 105871030
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 170, 'group_order': 96, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 3, 'size': 2}
  • id: 105871031
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 170, 'group_order': 96, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 51, 'size': 2}
  • id: 105871032
    {'aut_label': '2F', 'centralizer': '4.b1.a1', 'counter': 7, 'group_counter': 170, 'group_order': 96, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 33, 'size': 4}
  • id: 105871033
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 170, 'group_order': 96, 'label': '3A1', 'order': 3, 'powers': [9, 1], 'representative': 2, 'size': 1}
  • id: 105871034
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 170, 'group_order': 96, 'label': '3A-1', 'order': 3, 'powers': [8, 1], 'representative': 4, 'size': 1}
  • id: 105870994
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 170, 'group_order': 96, 'label': '4A1', 'order': 4, 'powers': [2, 11], 'representative': 18, 'size': 2}
  • id: 105870995
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 170, 'group_order': 96, 'label': '4A-1', 'order': 4, 'powers': [2, 10], 'representative': 6, 'size': 2}
  • id: 105870996
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 170, 'group_order': 96, 'label': '4B1', 'order': 4, 'powers': [2, 13], 'representative': 21, 'size': 2}
  • id: 105870997
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 170, 'group_order': 96, 'label': '4B-1', 'order': 4, 'powers': [2, 12], 'representative': 9, 'size': 2}
  • id: 105870998
    {'aut_label': '4C', 'centralizer': '4.d1.a1', 'counter': 14, 'group_counter': 170, 'group_order': 96, 'label': '4C', 'order': 4, 'powers': [3, 14], 'representative': 72, 'size': 4}
  • id: 105870999
    {'aut_label': '4C', 'centralizer': '4.d1.b1', 'counter': 15, 'group_counter': 170, 'group_order': 96, 'label': '4D', 'order': 4, 'powers': [4, 15], 'representative': 87, 'size': 4}
  • id: 105871000
    {'aut_label': '4E', 'centralizer': '4.e1.a1', 'counter': 16, 'group_counter': 170, 'group_order': 96, 'label': '4E', 'order': 4, 'powers': [2, 16], 'representative': 42, 'size': 4}
  • id: 105871001
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 170, 'group_order': 96, 'label': '6A1', 'order': 6, 'powers': [8, 2], 'representative': 16, 'size': 1}
  • id: 105871002
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 170, 'group_order': 96, 'label': '6A-1', 'order': 6, 'powers': [9, 2], 'representative': 14, 'size': 1}
  • id: 105871003
    {'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 170, 'group_order': 96, 'label': '6B1', 'order': 6, 'powers': [8, 3], 'representative': 52, 'size': 1}
  • id: 105871005
    {'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 170, 'group_order': 96, 'label': '6B-1', 'order': 6, 'powers': [9, 3], 'representative': 50, 'size': 1}
  • id: 105871006
    {'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 170, 'group_order': 96, 'label': '6C1', 'order': 6, 'powers': [9, 4], 'representative': 62, 'size': 1}
  • id: 105871007
    {'aut_label': '6B1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 170, 'group_order': 96, 'label': '6C-1', 'order': 6, 'powers': [8, 4], 'representative': 64, 'size': 1}
  • id: 105871008
    {'aut_label': '6D1', 'centralizer': '2.b1.a1', 'counter': 23, 'group_counter': 170, 'group_order': 96, 'label': '6D1', 'order': 6, 'powers': [8, 5], 'representative': 1, 'size': 2}
  • id: 105871009
    {'aut_label': '6D1', 'centralizer': '2.b1.a1', 'counter': 24, 'group_counter': 170, 'group_order': 96, 'label': '6D-1', 'order': 6, 'powers': [9, 5], 'representative': 5, 'size': 2}
  • id: 105871010
    {'aut_label': '6D1', 'centralizer': '2.b1.a1', 'counter': 25, 'group_counter': 170, 'group_order': 96, 'label': '6E1', 'order': 6, 'powers': [8, 6], 'representative': 49, 'size': 2}
  • id: 105871011
    {'aut_label': '6D1', 'centralizer': '2.b1.a1', 'counter': 26, 'group_counter': 170, 'group_order': 96, 'label': '6E-1', 'order': 6, 'powers': [9, 6], 'representative': 53, 'size': 2}
  • id: 105871012
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 27, 'group_counter': 170, 'group_order': 96, 'label': '6F1', 'order': 6, 'powers': [8, 7], 'representative': 31, 'size': 4}
  • id: 105871013
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 28, 'group_counter': 170, 'group_order': 96, 'label': '6F-1', 'order': 6, 'powers': [9, 7], 'representative': 35, 'size': 4}
  • id: 105871014
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 170, 'group_order': 96, 'label': '12A1', 'order': 12, 'powers': [17, 10], 'representative': 8, 'size': 2}
  • id: 105871016
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 170, 'group_order': 96, 'label': '12A-1', 'order': 12, 'powers': [18, 11], 'representative': 22, 'size': 2}
  • id: 105871017
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 31, 'group_counter': 170, 'group_order': 96, 'label': '12A5', 'order': 12, 'powers': [18, 10], 'representative': 10, 'size': 2}
  • id: 105871018
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 170, 'group_order': 96, 'label': '12A-5', 'order': 12, 'powers': [17, 11], 'representative': 20, 'size': 2}
  • id: 105871019
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 170, 'group_order': 96, 'label': '12B1', 'order': 12, 'powers': [18, 12], 'representative': 7, 'size': 2}
  • id: 105871020
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 170, 'group_order': 96, 'label': '12B-1', 'order': 12, 'powers': [17, 13], 'representative': 59, 'size': 2}
  • id: 105871021
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 170, 'group_order': 96, 'label': '12B5', 'order': 12, 'powers': [17, 12], 'representative': 11, 'size': 2}
  • id: 105871022
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 170, 'group_order': 96, 'label': '12B-5', 'order': 12, 'powers': [18, 13], 'representative': 55, 'size': 2}
  • id: 105871023
    {'aut_label': '12C1', 'centralizer': '4.d1.a1', 'counter': 37, 'group_counter': 170, 'group_order': 96, 'label': '12C1', 'order': 12, 'powers': [19, 14], 'representative': 26, 'size': 4}
  • id: 105871024
    {'aut_label': '12C1', 'centralizer': '4.d1.a1', 'counter': 38, 'group_counter': 170, 'group_order': 96, 'label': '12C-1', 'order': 12, 'powers': [20, 14], 'representative': 28, 'size': 4}
  • id: 105871025
    {'aut_label': '12C1', 'centralizer': '4.d1.b1', 'counter': 39, 'group_counter': 170, 'group_order': 96, 'label': '12D1', 'order': 12, 'powers': [21, 15], 'representative': 25, 'size': 4}
  • id: 105871027
    {'aut_label': '12C1', 'centralizer': '4.d1.b1', 'counter': 40, 'group_counter': 170, 'group_order': 96, 'label': '12D-1', 'order': 12, 'powers': [22, 15], 'representative': 29, 'size': 4}
  • id: 105871028
    {'aut_label': '12E1', 'centralizer': '4.e1.a1', 'counter': 41, 'group_counter': 170, 'group_order': 96, 'label': '12E1', 'order': 12, 'powers': [17, 16], 'representative': 32, 'size': 4}
  • id: 105871029
    {'aut_label': '12E1', 'centralizer': '4.e1.a1', 'counter': 42, 'group_counter': 170, 'group_order': 96, 'label': '12E-1', 'order': 12, 'powers': [18, 16], 'representative': 34, 'size': 4}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 3635009
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635020
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 3635026
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 3635027
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 3635028
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 3635029
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635030
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3635031
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3635032
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3635010
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -1, -1, -2, -2, 2, 2, 2, -2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 3635011
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -1, -1, 2, 2, -2, -2, 2, 2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 3635012
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -1, -1, -2, -2, 2, 2, -2, 2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 3635013
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -1, -1, 2, 2, -2, -2, -2, -2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 3635014
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -1, -1, -2, -2, -2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3635015
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -1, -1, 2, 2, 2, 2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635016
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -2, -2, -2, -2, 2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635017
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 3635018
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 3635019
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2c', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3635021
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2d', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3635022
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2e', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 3635023
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2f', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 3635024
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2g', 'multiplicity': 4, 'nt': [24, 17], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3635025
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '96.170', 'group_order': 96, 'image': None, 'label': '96.170.2h', 'multiplicity': 4, 'nt': [24, 17], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 5236114
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 96, 'label': '96.170.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5236125
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.b1', 'kernel_order': 48, 'label': '96.170.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5236136
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 48, 'label': '96.170.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5236147
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 48, 'label': '96.170.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5236151
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 48, 'label': '96.170.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5236152
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 48, 'label': '96.170.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5236153
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 48, 'label': '96.170.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5236154
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 48, 'label': '96.170.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5236155
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 32, 'label': '96.170.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]]]}
  • id: 5236115
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 32, 'label': '96.170.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]]]}
  • id: 5236116
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.b1', 'kernel_order': 16, 'label': '96.170.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]]]}
  • id: 5236117
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.b1', 'kernel_order': 16, 'label': '96.170.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]]]}
  • id: 5236118
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 16, 'label': '96.170.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]]]}
  • id: 5236119
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 16, 'label': '96.170.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]]]}
  • id: 5236120
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 16, 'label': '96.170.1l1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]]]}
  • id: 5236121
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 16, 'label': '96.170.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]]]}
  • id: 5236122
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 16, 'label': '96.170.1m1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]]]}
  • id: 5236123
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 16, 'label': '96.170.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]]]}
  • id: 5236124
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 16, 'label': '96.170.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]]]}
  • id: 5236126
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 16, 'label': '96.170.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]]]}
  • id: 5236127
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 16, 'label': '96.170.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
  • id: 5236128
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 16, 'label': '96.170.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
  • id: 5236129
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 16, 'label': '96.170.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]]]}
  • id: 5236130
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 96, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 16, 'label': '96.170.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]]]}
  • id: 5236131
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 12, 'label': '96.170.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236132
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 12, 'label': '96.170.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236133
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 6, 'label': '96.170.2c1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236134
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 6, 'label': '96.170.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236135
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 6, 'label': '96.170.2d1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236137
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 6, 'label': '96.170.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236138
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 4, 'label': '96.170.2e1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, -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]]]}
  • id: 5236139
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 4, 'label': '96.170.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, 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]]]}
  • id: 5236140
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 4, 'label': '96.170.2f1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -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]]]}
  • id: 5236141
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 24, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 4, 'label': '96.170.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 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]]]}
  • id: 5236142
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 35, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 2, 'label': '96.170.2g1', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236143
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 36, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 2, 'label': '96.170.2g2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[2, 2]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236144
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 37, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 2, 'label': '96.170.2g3', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236145
    {'center': '4.c1.b1', 'center_index': 4, 'center_order': 24, 'counter': 38, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.b1', 'kernel_order': 2, 'label': '96.170.2g4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[2, 2]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236146
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 39, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 2, 'label': '96.170.2h1', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236148
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 40, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 2, 'label': '96.170.2h2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236149
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 41, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 2, 'label': '96.170.2h3', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5236150
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 24, 'counter': 42, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '96.170', 'group_counter': 170, 'group_order': 96, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 2, 'label': '96.170.2h4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 59998808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '96.170.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.170', 'subgroup_hash': 170, 'subgroup_order': 96, 'subgroup_tex': '(C_2^2\\times C_{12}):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 48, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 48, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.2.e1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '96.170.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 2}
  • id: 59998809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 59998816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998828
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U1'], 'split': False, '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: 59998829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 59998831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 59998832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.8.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998833
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998834
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998835
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998840
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 59998843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.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': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.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': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': 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: 59998848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59998850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.12.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.12.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 6, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 53, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.16.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998860
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.16.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59998861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.24.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': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59998862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_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: 59998864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.170.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_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: 59998865
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59998866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.24.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59998870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 59998871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.24.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59998872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.170.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 59998873
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.24.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59998875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': 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: 59998876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 3, 'counter': 71, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '96.170.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 59998877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 2, 'counter': 72, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998879
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.170.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998882
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.170.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59998883
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.170', 'ambient_counter': 170, 'ambient_order': 96, 'ambient_tex': '(C_2^2\\times C_{12}):C_2', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '96.170.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '96.170', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2^2\\times C_{12}):C_2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', '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: 59998880
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.b1.a1', '24.f1.a1', '24.f1.b1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3735, -1, 6948, -1, 6891, -1, 5213, -1], 'generators': [3], 'label': '96.170.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998808
    {'ambient': '96.170', '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': '8.a1.a1', 'complements': ['96.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.e1.a1', '2.e1.b1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6092, 5997, 3596, 5384, 5330, 5411, 3675, 5424], 'generators': [3, 48, 12, 6, 24, 2], 'label': '96.170.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.e1.a1', '2.e1.b1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '8.5', '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': '8.5'}
  • id: 59998809
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.f1.a1', '8.f1.b1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3741, 8630, 8489, 420, 7267, 9502, 6332, 9639], 'generators': [3, 12, 48, 2], 'label': '96.170.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998810
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.g1.a1', '8.g1.b1', '12.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2018, 4585, 5162, 7225, 1142, 4660, 1022, 7135], 'generators': [33, 12, 48, 2], 'label': '96.170.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998811
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '12.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 3357, 5717, 4803, 3514, 3516, 3747, 8810], 'generators': [6, 48, 2, 12], 'label': '96.170.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998812
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.d1.b1', '12.c1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 3357, 4471, 1386, 3514, 3516, 5755, 6305], 'generators': [9, 48, 2, 12], 'label': '96.170.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998813
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '12.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2879, 2107, 2427, 6024, 2012, 2350, 444, 4060], 'generators': [12, 24, 2, 48], 'label': '96.170.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998814
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '4.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.h1.b1', '12.d1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2879, 2107, 3204, 2370, 2012, 2350, 2415, 7965], 'generators': [27, 48, 2, 60], 'label': '96.170.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998815
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.e1.a1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.e1.a1', '12.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5752, 557, 3905, 3819, 4400, 519, 4671, 3215], 'generators': [30, 48, 2, 12], 'label': '96.170.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.e1.a1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998816
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.e1.a1', '12.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4531, -1, 6372, -1, 5722, -1, 7924, -1], 'generators': [3, 30, 2, 12], 'label': '96.170.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998817
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.e1.a1', '12.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4531, -1, 6848, -1, 5722, -1, 7430, -1], 'generators': [51, 30, 2, 12], 'label': '96.170.4.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998818
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1', '12.g1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7717, -1, 7368, -1, 9606, -1, 9155, -1], 'generators': [3, 6, 2, 12], 'label': '96.170.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.g1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998819
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 4, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.f1.a1', '4.f1.b1', '6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5683, 5659, 5144, 4925, 4890, 4810, 5217, 5849], 'generators': [3, 12, 30, 48, 2], 'label': '96.170.2.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.e1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '8.5', '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': '8.5'}
  • id: 59998820
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.b1', '8.d1.a1', '8.d1.b1', '12.g1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7717, -1, 7934, -1, 9606, -1, 8567, -1], 'generators': [51, 6, 2, 12], 'label': '96.170.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.g1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998821
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7006, 6128, 3336, 7352, 6467, 6520, 5213, 1851], 'generators': [3, 30, 48], 'label': '96.170.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '24.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998822
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8, 'centralizer': '2.b1.a1', 'complements': ['16.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.c1.b1', '12.g1.a1', '12.g1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9682, 8123, 4256, 4212, 8735, 8380, 6899, 5476], 'generators': [3, 6, 48], 'label': '96.170.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998823
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': ['16.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.d1.b1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6334, 7086, 165, 6362, 8001, 7414, 1917, 2499], 'generators': [3, 24], 'label': '96.170.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.d1.b1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998824
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16, 'centralizer': '8.a1.a1', 'complements': ['16.c1.a1', '16.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.b1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5726, 5169, 1941, 9580, 2763, 5626, 2913, 4776], 'generators': [27, 6], 'label': '96.170.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998881
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.b1.b1', '24.f1.a1', '24.f1.b1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3735, -1, 7198, -1, 6891, -1, 4935, -1], 'generators': [51], 'label': '96.170.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.c1.b1', 'projective_image': '96.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998825
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16, 'centralizer': '8.a1.a1', 'complements': ['16.c1.a1', '16.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.b1', '12.d1.a1'], 'core': '6.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5726, 5169, 1414, 8898, 2763, 5626, 1509, 1203], 'generators': [9, 24], 'label': '96.170.6.d1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.b1', 'normal_contained_in': ['2.d1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.b1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998826
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16, 'centralizer': '8.a1.a1', 'complements': ['16.c1.a1', '16.c1.b1', '16.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.e1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8805, 3503, 738, 8046, 5097, 1434, 3285, 192], 'generators': [6, 24], 'label': '96.170.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.e1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998827
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16, 'centralizer': '8.a1.a1', 'complements': ['16.c1.a1', '16.c1.b1', '16.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.b1', '3.a1.a1'], 'contains': ['12.c1.b1', '12.d1.b1', '12.e1.a1'], 'core': '6.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8805, 3503, 1056, 4967, 5097, 1434, 4209, 669], 'generators': [27, 30], 'label': '96.170.6.e1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.b1', 'normal_contained_in': ['2.e1.b1', '3.a1.a1'], 'normal_contains': ['12.c1.b1', '12.e1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998828
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3191, 1960, 5560, 2406, 2725, 3594, 3108, 6316], 'generators': [12, 48, 2], 'label': '96.170.8.a1.a1', 'mobius_quo': -2, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.e1.a1', '4.d1.b1', '4.d1.a1'], 'normal_contains': ['16.b1.b1', '16.b1.a1', '16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '8.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998829
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '24.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3923, 9443, 8288, 1241, 7772, 7979, 8170, 7726], 'generators': [3, 12, 2], 'label': '96.170.8.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.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998830
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 4, 'centralizer': '2.b1.a1', 'complements': ['48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.g1.a1', '4.g1.b1', '6.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7448, 8630, 6068, 1802, 7865, 8723, 6332, 8634], 'generators': [3, 12, 6, 48, 2], 'label': '96.170.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998831
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.a1.a1', '16.c1.b1', '24.b1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3923, 9443, 8892, 420, 7772, 7979, 7679, 7021], 'generators': [51, 12, 2], 'label': '96.170.8.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.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998832
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '16.d1.a1', '24.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1523, -1, 6942, -1, 1539, -1, 6350, -1], 'generators': [33, 12, 2], 'label': '96.170.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '16.11', '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: 59998833
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.a1.a1', '24.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7658, -1, 7462, -1, 4814, -1, 9065, -1], 'generators': [6, 2, 12], 'label': '96.170.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '16.11', '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': '1.1'}
  • id: 59998834
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.a1.a1', '24.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7658, -1, 7899, -1, 4814, -1, 9383, -1], 'generators': [9, 2, 12], 'label': '96.170.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.b1', 'projective_image': '16.11', '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': '1.1'}
  • id: 59998835
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '24.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4935, -1, 6553, -1, 5292, -1, 7274, -1], 'generators': [30, 2, 12], 'label': '96.170.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998836
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.c1.b1', '24.f1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2255, -1, 9363, -1, 7033, -1, 4581, -1], 'generators': [3, 48, 2], 'label': '96.170.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998837
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.b1', '16.c1.a1', '16.c1.b1', '24.f1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2255, -1, 9835, -1, 7033, -1, 5563, -1], 'generators': [3, 60, 2], 'label': '96.170.8.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998838
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '24.g1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [318, -1, 4562, -1, 321, -1, 531, -1], 'generators': [33, 48, 2], 'label': '96.170.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.g1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998839
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.b1', '16.d1.a1', '24.g1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [318, -1, 6032, -1, 321, -1, 1022, -1], 'generators': [33, 60, 2], 'label': '96.170.8.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '8.g1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998840
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.b1.a1', '24.h1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [920, -1, 2549, -1, 930, -1, 126, -1], 'generators': [24, 2, 48], 'label': '96.170.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.h1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998841
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 4, 'centralizer': '8.a1.a1', 'complements': ['48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '6.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4806, 7203, 2090, 3940, 5776, 7392, 2025, 6694], 'generators': [3, 48, 24, 2, 12], 'label': '96.170.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.b1', '4.d1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998842
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1'], 'contains': ['16.b1.b1', '24.h1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [920, -1, 4172, -1, 930, -1, 1917, -1], 'generators': [27, 2, 60], 'label': '96.170.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '8.h1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998882
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.c1.a1', '24.g1.a1', '24.g1.b1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2701, -1, 5099, -1, 2622, -1, 2928, -1], 'generators': [33], 'label': '96.170.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '96.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998843
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1', '24.f1.a1', '24.f1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5936, 7086, 6435, 3192, 8365, 7199, 5957, 5605], 'generators': [3, 12, 48], 'label': '96.170.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998844
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.g1.a1', '24.g1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4353, 5843, 2181, 8439, 2132, 6320, 2224, 3770], 'generators': [33, 12, 48], 'label': '96.170.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.d1.b1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '24.15', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998845
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8266, 5008, 2559, 6374, 4204, 5540, 3599, 5040], 'generators': [6, 48], 'label': '96.170.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998846
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.d1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8266, 5008, 3031, 3850, 4204, 5540, 5072, 3205], 'generators': [9, 48], 'label': '96.170.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.c1.b1', '6.b1.a1', '6.d1.b1', '6.e1.b1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '24.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998847
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.h1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5145, 3964, 605, 7521, 3465, 4567, 1513, 2499], 'generators': [12, 24], 'label': '96.170.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.b1', '6.e1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '24.15', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998848
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '4.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.c1.a1', '6.d1.a1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.h1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5145, 3964, 1171, 4670, 3465, 4567, 2617, 4335], 'generators': [27, 48], 'label': '96.170.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.d1.b1', '6.c1.a1', '6.d1.a1', '6.e1.b1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '24.15', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998849
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '12.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.e1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7114, 2920, 1671, 5492, 5901, 2071, 4090, 1794], 'generators': [30, 48], 'label': '96.170.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '24.15', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998850
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6555, -1, 3920, -1, 6467, -1, 6986, -1], 'generators': [3, 30], 'label': '96.170.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '48.45', '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': '4.2'}
  • id: 59998851
    {'ambient': '96.170', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 64, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.a1.a1'], 'contains': ['24.b1.b1', '24.c1.a1', '24.e1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6555, -1, 4301, -1, 6467, -1, 6726, -1], 'generators': [51, 30], 'label': '96.170.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '48.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59998852
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': ['48.c1.a1', '48.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.b1', '6.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3794, 4362, 4558, 8052, 2763, 3644, 2704, 7669], 'generators': [27, 48, 6, 2, 60], 'label': '96.170.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.b1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998853
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.d1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9111, -1, 5321, -1, 8958, -1, 9787, -1], 'generators': [3, 6], 'label': '96.170.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.45', '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: 59998854
    {'ambient': '96.170', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.b1.a1'], 'contains': ['24.b1.b1', '24.d1.a1', '24.d1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9111, -1, 5925, -1, 8958, -1, 8661, -1], 'generators': [51, 6], 'label': '96.170.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.g1.b1', 'projective_image': '48.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998855
    {'ambient': '96.170', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1'], 'contains': ['32.a1.a1', '48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3304, 2222, 7920, 1060, 3911, 5604, 7274, 7021], 'generators': [12, 2], 'label': '96.170.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '16.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998856
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '16.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1475, 1670, 5106, 1724, 2681, 4503, 2668, 5849], 'generators': [48, 2], 'label': '96.170.16.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998857
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '16.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.b1', '8.g1.b1', '8.h1.b1'], 'contains': ['32.a1.a1', '48.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1475, 1670, 7334, 2455, 2681, 4503, 3448, 6648], 'generators': [60, 2], 'label': '96.170.16.b1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998858
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.f1.b1'], 'contains': ['32.a1.a1', '48.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2066, -1, 9339, -1, 6685, -1, 5213, -1], 'generators': [3, 2], 'label': '96.170.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.30', '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': '1.1'}
  • id: 59998859
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.f1.a1', '8.f1.b1'], 'contains': ['32.a1.a1', '48.c1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2066, -1, 9589, -1, 6685, -1, 4657, -1], 'generators': [51, 2], 'label': '96.170.16.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.c1.b1', 'projective_image': '32.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998860
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.g1.a1', '8.g1.b1'], 'contains': ['32.a1.a1', '48.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [603, -1, 7584, -1, 1713, -1, 2928, -1], 'generators': [33, 2], 'label': '96.170.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.d1.a1', 'projective_image': '32.30', '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': '1.1'}
  • id: 59998861
    {'ambient': '96.170', 'aut_centralizer_order': 128, 'aut_label': '24.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.c1.b1', '12.d1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4887, 3810, 3333, 3850, 4330, 5054, 3726, 5024], 'generators': [12, 48], 'label': '96.170.24.a1.a1', 'mobius_quo': 2, 'mobius_sub': 8, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.c1.b1', '12.e1.a1', '12.d1.b1', '12.d1.a1'], 'normal_contains': ['48.b1.b1', '48.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.15', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998862
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.c1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5662, 7086, 5817, 3113, 7696, 7199, 7553, 6248], 'generators': [3, 12], 'label': '96.170.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '48.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998863
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': ['48.c1.a1', '48.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.d1.a1', '6.d1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3794, 4362, 3905, 6917, 2763, 3644, 1347, 5004], 'generators': [9, 48, 24, 2, 12], 'label': '96.170.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.d1.a1', '6.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998864
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.a1.a1', '12.f1.b1', '12.g1.b1'], 'contains': ['48.a1.a1', '48.c1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5662, 7086, 6616, 2316, 7696, 7199, 6997, 5450], 'generators': [51, 12], 'label': '96.170.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.b1.b1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '48.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998865
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '48.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4418, -1, 4214, -1, 3492, -1, 6397, -1], 'generators': [33, 12], 'label': '96.170.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '48.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998866
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7933, -1, 5550, -1, 4759, -1, 8531, -1], 'generators': [6], 'label': '96.170.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.45', '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: 59998867
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.c1.b1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7933, -1, 6084, -1, 4759, -1, 8791, -1], 'generators': [9], 'label': '96.170.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.b1', 'projective_image': '48.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998868
    {'ambient': '96.170', 'aut_centralizer_order': 64, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6469, -1, 4513, -1, 5597, -1, 6718, -1], 'generators': [30], 'label': '96.170.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '48.45', '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': '2.1'}
  • id: 59998869
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.c1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3762, -1, 7032, -1, 7104, -1, 4935, -1], 'generators': [3, 48], 'label': '96.170.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '48.47', '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': '1.1'}
  • id: 59998870
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '12.a1.a1'], 'contains': ['48.b1.b1', '48.c1.a1', '48.c1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3762, -1, 7317, -1, 7104, -1, 5491, -1], 'generators': [3, 60], 'label': '96.170.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.b1', 'projective_image': '48.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998871
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '48.d1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2503, -1, 3635, -1, 2219, -1, 2094, -1], 'generators': [33, 48], 'label': '96.170.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.g1.a1', 'projective_image': '48.47', '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': '2.1'}
  • id: 59998872
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '12.b1.a1'], 'contains': ['48.b1.b1', '48.d1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2503, -1, 3923, -1, 2219, -1, 2390, -1], 'generators': [33, 60], 'label': '96.170.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '24.g1.b1', 'projective_image': '48.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998873
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.d1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3143, -1, 1972, -1, 3073, -1, 1513, -1], 'generators': [24], 'label': '96.170.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.h1.a1', 'projective_image': '48.47', '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': '2.1'}
  • id: 59998874
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': ['48.c1.a1', '48.c1.b1', '48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '6.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6502, 2107, 2708, 5842, 4063, 2350, 3347, 3215], 'generators': [6, 48, 24, 2, 12], 'label': '96.170.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.d1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998875
    {'ambient': '96.170', 'aut_centralizer_order': 32, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '4.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.d1.b1'], 'contains': ['48.b1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3143, -1, 2278, -1, 3073, -1, 3188, -1], 'generators': [27], 'label': '96.170.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '24.h1.b1', 'projective_image': '48.47', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59998876
    {'ambient': '96.170', 'aut_centralizer_order': 128, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.c1.a1', '16.c1.b1', '16.d1.a1'], 'contains': ['96.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1975, 2222, 7854, 1869, 3111, 5089, 4419, 6632], 'generators': [2], 'label': '96.170.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.b1', '16.b1.a1', '16.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.30', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998877
    {'ambient': '96.170', 'aut_centralizer_order': 256, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1'], 'contains': ['96.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4903, 3672, 5966, 2443, 4330, 5604, 6997, 6248], 'generators': [12], 'label': '96.170.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.45', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.45', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998878
    {'ambient': '96.170', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1'], 'contains': ['96.a1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3235, 2943, 3968, 2877, 3503, 4574, 2668, 5502], 'generators': [48], 'label': '96.170.48.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '48.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.47', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998879
    {'ambient': '96.170', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.a1', '24.f1.b1', '24.g1.b1', '24.h1.b1'], 'contains': ['96.a1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3235, 2943, 4711, 3475, 3503, 4574, 3585, 5875], 'generators': [60], 'label': '96.170.48.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.b1', 'projective_image': '48.47', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.47', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998883
    {'ambient': '96.170', 'aut_centralizer_order': None, 'aut_label': '96.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': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.c1.a1', '48.c1.b1', '48.d1.a1'], 'contains': [], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3235, 2943, 5966, 2660, 3503, 5089, 4419, 6062], 'generators': [], 'label': '96.170.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.b1', '48.b1.a1', '48.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59998884
    {'ambient': '96.170', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 8, 'centralizer': '8.a1.a1', 'complements': ['48.c1.a1', '48.c1.b1', '48.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.b1', '4.e1.a1', '6.e1.b1'], 'core': '2.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6502, 2107, 3287, 2865, 4063, 2350, 4668, 4081], 'generators': [27, 48, 30, 2, 60], 'label': '96.170.2.e1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.e1.a1', '4.d1.b1', '6.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59998885
    {'ambient': '96.170', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2, 'centralizer': '8.a1.a1', 'complements': ['32.a1.a1'], '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': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8455, 6727, 1571, 8735, 6826, 6012, 4007, 2059], 'generators': [3, 6, 24], 'label': '96.170.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '24.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}