Abstract group data - 48.14

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 2, 2, 6], 'aut_gens': [[1, 2, 4], [3, 2, 4], [25, 2, 4], [25, 2, 6], [1, 2, 20], [41, 2, 28]], 'aut_group': '96.230', 'aut_hash': 230, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 11, 'aut_perms': [5167, 1, 288, 363007, 3991806], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 2, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [6, 2, 1, 3], [12, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [3, 2, 1], [4, 2, 2], [4, 6, 2], [6, 2, 3], [12, 2, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [3, 2, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [6, 2, 1, 3], [12, 2, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '12.4', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 1, 6], 'inner_gens': [[1, 2, 22], [1, 2, 4], [35, 2, 4]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10]], 'label': '48.14', 'linC_count': 16, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 18, 'linQ_dim': 6, 'linQ_dim_count': 18, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D6:C4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 18, 'number_divisions': 13, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 34, 'number_subgroups': 76, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 16], [6, 6], [12, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 2, 28], [1, 2, 6], [25, 2, 4]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 3]], 'representations': {'PC': {'code': 2914833145217, 'gens': [1, 2, 3], 'pres': [5, -2, -2, 2, -2, -3, 332, 42, 803, 58, 804]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101738376610178, 91655872448018982]}, 'GLFp': {'d': 3, 'p': 13, 'gens': [5650246730, 9789111396, 2629817970, 10109304234, 8744930337]}, 'Perm': {'d': 11, 'gens': [3807481, 8406960, 3719544, 12541704, 3]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_6:C_4', 'transitive_degree': 24, '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: 105373157
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 14, 'group_order': 48, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 105373167
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 14, 'group_order': 48, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 26, 'size': 1}
  • id: 105373168
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 14, 'group_order': 48, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2, 'size': 1}
  • id: 105373169
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 14, 'group_order': 48, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 24, 'size': 1}
  • id: 105373170
    {'aut_label': '2D', 'centralizer': '6.b1.a1', 'counter': 5, 'group_counter': 14, 'group_order': 48, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 6}
  • id: 105373171
    {'aut_label': '2D', 'centralizer': '6.b1.a1', 'counter': 6, 'group_counter': 14, 'group_order': 48, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 9, 'size': 6}
  • id: 105373172
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 7, 'group_counter': 14, 'group_order': 48, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 32, 'size': 2}
  • id: 105373173
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 14, 'group_order': 48, 'label': '4A1', 'order': 4, 'powers': [4, 9], 'representative': 12, 'size': 2}
  • id: 105373174
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 14, 'group_order': 48, 'label': '4A-1', 'order': 4, 'powers': [4, 8], 'representative': 36, 'size': 2}
  • id: 105373158
    {'aut_label': '4B1', 'centralizer': '6.c1.a1', 'counter': 10, 'group_counter': 14, 'group_order': 48, 'label': '4B1', 'order': 4, 'powers': [2, 11], 'representative': 5, 'size': 6}
  • id: 105373159
    {'aut_label': '4B1', 'centralizer': '6.c1.a1', 'counter': 11, 'group_counter': 14, 'group_order': 48, 'label': '4B-1', 'order': 4, 'powers': [2, 10], 'representative': 13, 'size': 6}
  • id: 105373160
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 14, 'group_order': 48, 'label': '6A', 'order': 6, 'powers': [7, 3], 'representative': 18, 'size': 2}
  • id: 105373161
    {'aut_label': '6B', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 14, 'group_order': 48, 'label': '6B', 'order': 6, 'powers': [7, 2], 'representative': 10, 'size': 2}
  • id: 105373162
    {'aut_label': '6C', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 14, 'group_order': 48, 'label': '6C', 'order': 6, 'powers': [7, 4], 'representative': 8, 'size': 2}
  • id: 105373163
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 14, 'group_order': 48, 'label': '12A1', 'order': 12, 'powers': [14, 8], 'representative': 4, 'size': 2}
  • id: 105373164
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 14, 'group_order': 48, 'label': '12A-1', 'order': 12, 'powers': [14, 9], 'representative': 44, 'size': 2}
  • id: 105373165
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 14, 'group_order': 48, 'label': '12A5', 'order': 12, 'powers': [14, 8], 'representative': 20, 'size': 2}
  • id: 105373166
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 14, 'group_order': 48, 'label': '12A-5', 'order': 12, 'powers': [14, 9], 'representative': 28, 'size': 2}
• 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: 3413167
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1a', '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], 'schur_index': 1}
  • id: 3413172
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1b', '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], 'schur_index': 1}
  • id: 3413173
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1c', '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], 'schur_index': 1}
  • id: 3413174
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1d', '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], 'schur_index': 1}
  • id: 3413175
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413176
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413177
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3413178
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413179
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413168
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -1, -2, -2, 0, 0, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3413169
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2e', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413170
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2f', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -2, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3413171
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '48.14', 'group_order': 48, 'image': None, 'label': '48.14.2g', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -2, 0, 0, 0, 0, -2, 2, 2, 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: 4779255
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 48, 'label': '48.14.1a', '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]]]}
  • id: 4779265
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 24, 'label': '48.14.1b', '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]]]}
  • id: 4779266
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 24, 'label': '48.14.1c', '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]]]}
  • id: 4779267
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 24, 'label': '48.14.1d', '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]]]}
  • id: 4779268
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 12, 'label': '48.14.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4779269
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 12, 'label': '48.14.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4779270
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 12, 'label': '48.14.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4779271
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 48, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 12, 'label': '48.14.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4779272
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 8, 'label': '48.14.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 4779256
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 6, 'label': '48.14.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4779257
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 6, 'label': '48.14.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4779258
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 4, 'label': '48.14.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 4779259
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 13, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 2, 'label': '48.14.2e1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4779260
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 8, 'counter': 14, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 2, 'label': '48.14.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4779261
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 4, 'counter': 15, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 2, 'label': '48.14.2f1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 4779262
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 4, 'counter': 16, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 2, 'label': '48.14.2f2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 4779263
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 4, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 2, 'label': '48.14.2g1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 4779264
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 4, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '48.14', 'group_counter': 14, 'group_order': 48, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 2, 'label': '48.14.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
• 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: 58569708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 48, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '48.14.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 24, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 24, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, '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': ['F'], 'split': True, '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: 58569736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 24, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '48.14.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 2}
  • id: 58569738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 12, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': ['S', 'C2'], '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: 58569739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569709
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '48.14.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58569712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, '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: 58569713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 58569714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 6, 'counter': 16, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.8.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': '8.3', '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569716
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 6, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], '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: 58569717
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 6, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58569718
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58569720
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58569721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 4, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48.14.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 58569722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58569723
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '48.14.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58569725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58569726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '48.14.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58569727
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '48.14.12.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58569728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '48.14.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C4'], '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: 58569729
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 2, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58569731
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 2, 'counter': 30, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', '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: 58569732
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 2, 'counter': 31, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '48.14.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58569733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '48.14.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 58569734
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '48.14.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 58569735
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '48.14', 'ambient_counter': 14, 'ambient_order': 48, 'ambient_tex': 'D_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 1, 'counter': 34, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '48.14.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '48.14', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 58569708
    {'ambient': '48.14', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.a1', 'complements': ['48.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6645, 4969, 6664, 5168, 6191, 4931, 6442, 4931], 'generators': [1, 16, 12, 2, 24], 'label': '48.14.1.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'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58569709
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '12.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6019, -1, 7382, -1, 9606, -1, 8332, -1], 'generators': [5, 26, 16], 'label': '48.14.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.d1.a1', 'projective_image': '24.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58569710
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.d1.b1', '12.e1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3248, -1, 3182, -1, 1819, -1, 1890, -1], 'generators': [1, 24, 16], 'label': '48.14.4.e1.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.e1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58569711
    {'ambient': '48.14', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '12.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7516, -1, 4973, -1, 5755, -1, 6152, -1], 'generators': [12, 16, 24], 'label': '48.14.4.f1.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.f1.a1', 'projective_image': '24.8', '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': '1.1'}
  • id: 58569712
    {'ambient': '48.14', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '2.b1.a1', 'complements': ['8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9713, 8281, 8519, 8859, 6947, 8132, 7233, 8218], 'generators': [2, 12], 'label': '48.14.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569713
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5902, -1, 5454, -1, 2638, -1, 3327, -1], 'generators': [1, 2, 24], 'label': '48.14.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569714
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7866, -1, 9754, -1, 8393, -1, 9431, -1], 'generators': [5, 24], 'label': '48.14.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569715
    {'ambient': '48.14', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2845, 5162, 6727, 5682, 6074, 5912, 6201, 4397], 'generators': [26, 16], 'label': '48.14.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569716
    {'ambient': '48.14', 'aut_centralizer_order': 48, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1', '24.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1051, 1979, 354, 2460, 1925, 2839, 4812, 2860], 'generators': [2, 16], 'label': '48.14.8.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['16.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569717
    {'ambient': '48.14', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '24.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3609, 3613, 3655, 4071, 4436, 4376, 5506, 5934], 'generators': [24, 16], 'label': '48.14.8.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '24.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569718
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [287, -1, 1009, -1, 1160, -1, 3327, -1], 'generators': [1, 16], 'label': '48.14.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '48.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58569719
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.e1.a1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4023, 1484, 3846, 1543, 3053, 1473, 3327, 1473], 'generators': [1, 2, 24, 16], 'label': '48.14.2.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.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '12.4', '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': '12.4'}
  • id: 58569720
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.c1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [287, -1, 2490, -1, 1160, -1, 260, -1], 'generators': [9, 16], 'label': '48.14.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '48.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58569721
    {'ambient': '48.14', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.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.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7080, 7119, 7354, 7829, 5255, 7556, 6943, 7577], 'generators': [2, 24], 'label': '48.14.12.a1.a1', 'mobius_quo': 2, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569722
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.d1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3769, -1, 5537, -1, 3617, -1, 2584, -1], 'generators': [1, 26], 'label': '48.14.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '24.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569723
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1'], 'contains': ['24.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6262, -1, 8055, -1, 8393, -1, 8380, -1], 'generators': [5], 'label': '48.14.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.c1.a1', 'projective_image': '24.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569724
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2898, -1, 463, -1, 340, -1, 4069, -1], 'generators': [1, 2], 'label': '48.14.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569725
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.d1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2898, -1, 3282, -1, 340, -1, 1003, -1], 'generators': [9, 2], 'label': '48.14.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569726
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.d1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5446, -1, 4373, -1, 2745, -1, 1794, -1], 'generators': [1, 24], 'label': '48.14.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569727
    {'ambient': '48.14', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1'], 'contains': ['24.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8789, -1, 6237, -1, 6840, -1, 7685, -1], 'generators': [12], 'label': '48.14.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569728
    {'ambient': '48.14', 'aut_centralizer_order': 48, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1210, 2344, 2063, 2863, 3691, 2946, 4118, 2967], 'generators': [16], 'label': '48.14.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58569729
    {'ambient': '48.14', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4405, 6624, 6736, 7315, 5255, 7556, 6201, 6041], 'generators': [26], 'label': '48.14.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.6', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569730
    {'ambient': '48.14', 'aut_centralizer_order': 12, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 12, 'centralizer': '2.b1.a1', 'complements': ['24.d1.a1', '24.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '6.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7516, 8516, 5909, 8859, 5457, 8453, 5776, 8453], 'generators': [2, 12, 16, 24], 'label': '48.14.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '12.4', '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: 58569731
    {'ambient': '48.14', 'aut_centralizer_order': 96, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['48.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3333, 3528, 2282, 4093, 2925, 4482, 4812, 4504], 'generators': [2], 'label': '48.14.24.b1.a1', 'mobius_quo': -1, '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': '24.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569732
    {'ambient': '48.14', 'aut_centralizer_order': 96, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6019, 5075, 5700, 5704, 4457, 6019, 5506, 7577], 'generators': [24], 'label': '48.14.24.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '24.8', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569733
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': '24T33', 'count': 6, 'diagramx': [2568, -1, 2937, -1, 2159, -1, 3327, -1], 'generators': [1], 'label': '48.14.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.14', '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: 58569734
    {'ambient': '48.14', 'aut_centralizer_order': 8, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.b1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': '24T33', 'count': 6, 'diagramx': [2568, -1, 3937, -1, 2159, -1, 1794, -1], 'generators': [9], 'label': '48.14.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.b1', 'projective_image': '48.14', '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: 58569735
    {'ambient': '48.14', 'aut_centralizer_order': None, 'aut_label': '48.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': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.d1.b1'], 'contains': [], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3333, 4301, 3691, 4900, 3691, 5251, 4465, 5272], 'generators': [], 'label': '48.14.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58569736
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': ['24.d1.a1', '24.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '6.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5764, 4969, 7409, 5168, 8415, 4931, 8457, 4931], 'generators': [5, 24, 26, 16], 'label': '48.14.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '12.4', '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': '12.4'}
  • id: 58569737
    {'ambient': '48.14', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8587, -1, 8664, -1, 6925, -1, 7107, -1], 'generators': [1, 12], 'label': '48.14.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 58569738
    {'ambient': '48.14', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, '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.c1.a1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4352, 4969, 5991, 5168, 4564, 4931, 5072, 5080], 'generators': [2, 24, 16], 'label': '48.14.4.a1.a1', 'mobius_quo': -2, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '12.4', '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: 58569739
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': ['12.f1.a1', '12.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '12.d1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [849, 1505, 246, 2751, 1053, 2284, 4069, 1323], 'generators': [1, 2, 16], 'label': '48.14.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58569740
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': ['12.f1.a1', '12.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.b1', '12.d1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [849, 1505, 1800, 1141, 1053, 2284, 1099, 2860], 'generators': [9, 2, 16], 'label': '48.14.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58569741
    {'ambient': '48.14', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '12.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2261, -1, 3846, -1, 3457, -1, 2584, -1], 'generators': [1, 26, 16], 'label': '48.14.4.c1.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.c1.a1', 'projective_image': '24.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}