Abstract group data - 96.219

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 3, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 16], [1, 3, 13, 80], [1, 10, 12, 80], [9, 10, 60, 80], [1, 2, 68, 16], [1, 2, 4, 80], [1, 10, 13, 88], [1, 3, 12, 80], [49, 50, 52, 80], [1, 2, 12, 80], [1, 2, 4, 81]], 'aut_group': '9216.mt', 'aut_hash': 286080303390451077, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9216, 'aut_permdeg': 19, 'aut_perms': [6423384153306832, 368047, 13516396735944376, 7257600, 362880, 40658485439169358, 47060859623868847, 186811003567, 6423384153276847, 44460928880209], 'aut_phi_ratio': 288.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 2, 4, 1], [2, 6, 4, 1], [3, 2, 1, 1], [4, 6, 4, 1], [6, 2, 1, 1], [6, 2, 6, 1], [6, 2, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times C_2^6:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '1536.408640869', 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_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, 7], [2, 2, 4], [2, 6, 4], [3, 2, 1], [4, 6, 4], [6, 2, 15]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, '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', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 219, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['24.8', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 6, 1, 4], [3, 2, 1, 1], [4, 6, 1, 4], [6, 2, 1, 7], [6, 2, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2730, 'exponent': 12, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '48.51', 'hash': 219, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 2, 3], 'inner_gens': [[1, 2, 4, 16], [1, 2, 12, 16], [1, 10, 4, 80], [1, 2, 36, 16]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20]], 'label': '96.219', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3:D6', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 36, 'number_divisions': 32, 'number_normal_subgroups': 105, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 236, 'number_subgroups': 498, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 39], [3, 2], [4, 24], [6, 30]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[49, 50, 52, 16], [49, 50, 52, 65], [1, 2, 5, 16], [1, 2, 52, 16], [1, 3, 5, 16], [1, 50, 52, 16], [1, 2, 4, 24], [9, 10, 4, 16], [1, 10, 4, 16]], 'outer_group': '768.1090231', 'outer_hash': 1090231, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [167328001, 174641884, 23, 7, 258829920, 167368440, 135732240, 167450520, 90842400], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5:S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 4]], 'representations': {'PC': {'code': 5822333237396737, 'gens': [1, 2, 3, 5], 'pres': [6, -2, -2, -2, -2, -2, -3, 116, 50, 616, 88, 593]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705943105991, 141602720900, 705686952884, 706461794101]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 8645, 9565, 2665, 1777, 1801]}, 'Perm': {'d': 11, 'gens': [3669847, 720, 721, 766801, 7983360, 30]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:D_6', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 105872071
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 219, 'group_order': 96, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 105872082
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 219, 'group_order': 96, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 8, 'size': 1}
  • id: 105872093
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 219, 'group_order': 96, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 48, 'size': 1}
  • id: 105872101
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 219, 'group_order': 96, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 56, 'size': 1}
  • id: 105872102
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 219, 'group_order': 96, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 1}
  • id: 105872103
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 219, 'group_order': 96, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 49, 'size': 1}
  • id: 105872104
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 219, 'group_order': 96, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 9, 'size': 1}
  • id: 105872105
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 219, 'group_order': 96, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 57, 'size': 1}
  • id: 105872106
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 219, 'group_order': 96, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 2, 'size': 2}
  • id: 105872072
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 10, 'group_counter': 219, 'group_order': 96, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 50, 'size': 2}
  • id: 105872073
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 11, 'group_counter': 219, 'group_order': 96, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 3, 'size': 2}
  • id: 105872074
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 12, 'group_counter': 219, 'group_order': 96, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 51, 'size': 2}
  • id: 105872075
    {'aut_label': '2L', 'centralizer': '6.c1', 'counter': 13, 'group_counter': 219, 'group_order': 96, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 6, 'size': 6}
  • id: 105872076
    {'aut_label': '2L', 'centralizer': '6.c1', 'counter': 14, 'group_counter': 219, 'group_order': 96, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 22, 'size': 6}
  • id: 105872077
    {'aut_label': '2L', 'centralizer': '6.c1', 'counter': 15, 'group_counter': 219, 'group_order': 96, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 7, 'size': 6}
  • id: 105872078
    {'aut_label': '2L', 'centralizer': '6.c1', 'counter': 16, 'group_counter': 219, 'group_order': 96, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 23, 'size': 6}
  • id: 105872079
    {'aut_label': '3A', 'centralizer': '2.b1', 'counter': 17, 'group_counter': 219, 'group_order': 96, 'label': '3A', 'order': 3, 'powers': [17, 1], 'representative': 32, 'size': 2}
  • id: 105872080
    {'aut_label': '4A', 'centralizer': '6.d1', 'counter': 18, 'group_counter': 219, 'group_order': 96, 'label': '4A', 'order': 4, 'powers': [2, 18], 'representative': 4, 'size': 6}
  • id: 105872081
    {'aut_label': '4A', 'centralizer': '6.d1', 'counter': 19, 'group_counter': 219, 'group_order': 96, 'label': '4B', 'order': 4, 'powers': [2, 19], 'representative': 20, 'size': 6}
  • id: 105872083
    {'aut_label': '4A', 'centralizer': '6.d1', 'counter': 20, 'group_counter': 219, 'group_order': 96, 'label': '4C', 'order': 4, 'powers': [2, 20], 'representative': 5, 'size': 6}
  • id: 105872084
    {'aut_label': '4A', 'centralizer': '6.d1', 'counter': 21, 'group_counter': 219, 'group_order': 96, 'label': '4D', 'order': 4, 'powers': [2, 21], 'representative': 21, 'size': 6}
  • id: 105872085
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 22, 'group_counter': 219, 'group_order': 96, 'label': '6A', 'order': 6, 'powers': [17, 3], 'representative': 16, 'size': 2}
  • id: 105872086
    {'aut_label': '6B', 'centralizer': '2.b1', 'counter': 23, 'group_counter': 219, 'group_order': 96, 'label': '6B', 'order': 6, 'powers': [17, 2], 'representative': 40, 'size': 2}
  • id: 105872087
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 24, 'group_counter': 219, 'group_order': 96, 'label': '6C', 'order': 6, 'powers': [17, 4], 'representative': 24, 'size': 2}
  • id: 105872088
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 25, 'group_counter': 219, 'group_order': 96, 'label': '6D', 'order': 6, 'powers': [17, 5], 'representative': 33, 'size': 2}
  • id: 105872089
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 26, 'group_counter': 219, 'group_order': 96, 'label': '6E', 'order': 6, 'powers': [17, 6], 'representative': 17, 'size': 2}
  • id: 105872090
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 27, 'group_counter': 219, 'group_order': 96, 'label': '6F', 'order': 6, 'powers': [17, 7], 'representative': 41, 'size': 2}
  • id: 105872091
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 28, 'group_counter': 219, 'group_order': 96, 'label': '6G', 'order': 6, 'powers': [17, 8], 'representative': 25, 'size': 2}
  • id: 105872092
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 29, 'group_counter': 219, 'group_order': 96, 'label': '6H1', 'order': 6, 'powers': [17, 9], 'representative': 34, 'size': 2}
  • id: 105872094
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 30, 'group_counter': 219, 'group_order': 96, 'label': '6H-1', 'order': 6, 'powers': [17, 9], 'representative': 66, 'size': 2}
  • id: 105872095
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 31, 'group_counter': 219, 'group_order': 96, 'label': '6I1', 'order': 6, 'powers': [17, 10], 'representative': 18, 'size': 2}
  • id: 105872096
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 32, 'group_counter': 219, 'group_order': 96, 'label': '6I-1', 'order': 6, 'powers': [17, 10], 'representative': 26, 'size': 2}
  • id: 105872097
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 33, 'group_counter': 219, 'group_order': 96, 'label': '6J1', 'order': 6, 'powers': [17, 11], 'representative': 35, 'size': 2}
  • id: 105872098
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 34, 'group_counter': 219, 'group_order': 96, 'label': '6J-1', 'order': 6, 'powers': [17, 11], 'representative': 67, 'size': 2}
  • id: 105872099
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 35, 'group_counter': 219, 'group_order': 96, 'label': '6K1', 'order': 6, 'powers': [17, 12], 'representative': 19, 'size': 2}
  • id: 105872100
    {'aut_label': '6H1', 'centralizer': '2.b1', 'counter': 36, 'group_counter': 219, 'group_order': 96, 'label': '6K-1', 'order': 6, 'powers': [17, 12], 'representative': 27, '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: 3635697
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635708
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635719
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635723
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635724
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635725
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3635726
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3635727
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3635728
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3635698
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3635699
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3635700
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3635701
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3635702
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635703
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3635704
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3635705
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3635706
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 2, -2, 0], 'schur_index': 1}
  • id: 3635707
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, -2, -2, 2, 0], 'schur_index': 1}
  • id: 3635709
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, 2, 0], 'schur_index': 1}
  • id: 3635710
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 2, -2, 0], 'schur_index': 1}
  • id: 3635711
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3635712
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3635713
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3635714
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 3635715
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 3635716
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3635717
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3635718
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2m', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, -2, 2, 0], 'schur_index': 1}
  • id: 3635720
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2n', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2, -2, 0], 'schur_index': 1}
  • id: 3635721
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2o', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 2, -2, 0], 'schur_index': 1}
  • id: 3635722
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '96.219', 'group_order': 96, 'image': None, 'label': '96.219.2p', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, -2, 2, 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: 5237192
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 96, 'label': '96.219.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237203
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237214
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237222
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237223
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237224
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237225
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237226
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237227
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237193
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237194
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237195
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237196
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 48, 'label': '96.219.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237197
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 48, 'label': '96.219.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237198
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 48, 'label': '96.219.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237199
    {'center': '1.a1', 'center_index': 1, 'center_order': 96, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 48, 'label': '96.219.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237200
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 16, 'label': '96.219.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237201
    {'center': '4.d1', 'center_index': 4, 'center_order': 24, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 12, 'label': '96.219.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 5237202
    {'center': '4.d1', 'center_index': 4, 'center_order': 24, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 12, 'label': '96.219.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]]]}
  • id: 5237204
    {'center': '4.d1', 'center_index': 4, 'center_order': 24, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 12, 'label': '96.219.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]]]}
  • id: 5237205
    {'center': '4.d1', 'center_index': 4, 'center_order': 24, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 12, 'label': '96.219.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 5237206
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5237207
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237208
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237209
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237210
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5237211
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 8, 'label': '96.219.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5237212
    {'center': '6.a1', 'center_index': 6, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 8, 'label': '96.219.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5237213
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2m1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]]]}
  • id: 5237215
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 5237216
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2n1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]]]}
  • id: 5237217
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 5237218
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2o1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 5237219
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2o2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]]]}
  • id: 5237220
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2p1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 5237221
    {'center': '12.b1', 'center_index': 12, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '96.219', 'group_counter': 219, 'group_order': 96, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 4, 'label': '96.219.2p2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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: 60000312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '96.219.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '96.219.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '96.219.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 60000357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, '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'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '96.219.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60000318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60000320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], '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: 60000322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], '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: 60000325
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60000326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000327
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, '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', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000336
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60000337
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 6, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.219.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], '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: 60000338
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.219.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000339
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.219.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60000340
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60000341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000342
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '96.219.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '96.219.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000346
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.219.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60000347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '96.219.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60000349
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 3, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '96.219.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 60000350
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 2, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96.219.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], '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: 60000351
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '96.219.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60000352
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.219.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60000353
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96.219.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60000354
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96.219', 'ambient_counter': 219, 'ambient_order': 96, 'ambient_tex': 'C_2^3:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '96.219.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '96.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 60000328
    {'ambient': '96.219', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 768, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.b1', '4.g1'], 'contains': ['16.b1', '16.d1', '24.g1'], 'core': '16.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4206, -1, 2842, -1], 'generators': [6, 48, 32], 'label': '96.219.8.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.g1', 'projective_image': '48.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60000312
    {'ambient': '96.219', '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.b1', 'complements': ['96.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '3.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4810, 4320, 4822, 5151], 'generators': [1, 32, 8, 2, 4, 48], 'label': '96.219.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1'], 'normalizer': '1.a1', 'old_label': '1.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', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000313
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 192, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.a1', '8.e1', '12.b1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2941, 1158, 3138, 8086], 'generators': [1, 8, 48, 32], 'label': '96.219.4.d1', 'mobius_quo': 8, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '8.e1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.d1', '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.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000314
    {'ambient': '96.219', 'aut_centralizer_order': 24, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 384, 'centralizer': '12.b1', 'complements': ['24.c1', '24.f1', '24.g1'], 'conjugacy_class_count': 16, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '12.e1'], 'core': '4.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [9240, 9257, 9751, 466], 'generators': [2, 84, 8, 32], 'label': '96.219.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '48.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000315
    {'ambient': '96.219', 'aut_centralizer_order': 24, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.48', 'aut_weyl_index': 192, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1'], 'contains': ['8.e1', '8.f1', '12.f1'], 'core': '8.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [478, -1, 1522, -1], 'generators': [1, 2, 48, 32], 'label': '96.219.4.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.f1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000316
    {'ambient': '96.219', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 64, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['8.e1', '8.g1', '12.g1'], 'core': '8.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [1860, -1, 465, -1], 'generators': [1, 6, 48, 32], 'label': '96.219.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.g1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60000317
    {'ambient': '96.219', 'aut_centralizer_order': 48, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 48, 'centralizer': '2.b1', 'complements': ['16.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.f1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2823, 2581, 3946, 9596], 'generators': [1, 2, 8, 48], 'label': '96.219.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '6.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', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000318
    {'ambient': '96.219', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.27', 'aut_weyl_index': 288, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.c1', '12.d1', '12.e1'], 'core': '12.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8105, -1, 7852, -1], 'generators': [2, 4, 48], 'label': '96.219.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60000319
    {'ambient': '96.219', 'aut_centralizer_order': 16, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 48, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.b1', '12.c1', '12.g1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3648, -1, 2330, -1], 'generators': [1, 6, 8, 48], 'label': '96.219.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000320
    {'ambient': '96.219', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 48, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.d1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5781, -1, 5805, -1], 'generators': [1, 4, 48], 'label': '96.219.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000321
    {'ambient': '96.219', 'aut_centralizer_order': 768, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'contains': ['16.a1', '16.b1', '24.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5444, 4144, 5562, 5340], 'generators': [8, 48, 32], 'label': '96.219.8.a1', 'mobius_quo': -2, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normal_contains': ['16.a1', '16.b1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000322
    {'ambient': '96.219', 'aut_centralizer_order': 576, 'aut_label': '8.b1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': ['12.g1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.e1'], 'contains': ['16.a1', '16.c1', '24.b1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7163, 7507, 8431, 3627], 'generators': [50, 8, 32], 'label': '96.219.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.e1'], 'normal_contains': ['16.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000323
    {'ambient': '96.219', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 48, 'centralizer': '12.b1', 'complements': ['48.b1', '48.c1', '48.d1'], 'conjugacy_class_count': 12, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.e1', '6.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7355, 7356, 7609, 2028], 'generators': [2, 32, 4, 48, 8], 'label': '96.219.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000324
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '8.c1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 768, 'centralizer': '12.b1', 'complements': ['12.f1'], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.e1'], 'contains': ['16.a1', '16.d1', '24.d1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7878, 8817, 6815, 1159], 'generators': [86, 8, 32], 'label': '96.219.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.e1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000325
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '8.d1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 768, 'centralizer': '12.b1', 'complements': ['12.f1', '12.g1'], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.e1'], 'contains': ['16.a1', '24.e1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9536, 6071, 9683, 2191], 'generators': [84, 8, 32], 'label': '96.219.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.e1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000326
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 768, 'centralizer': '2.b1', 'complements': ['12.e1'], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.f1', '4.g1'], 'contains': ['16.b1', '24.c1'], 'core': '8.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [464, 743, 1589, 8086], 'generators': [1, 48, 32], 'label': '96.219.8.e1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.d1'], 'normal_contains': ['16.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.e1', '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.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000327
    {'ambient': '96.219', 'aut_centralizer_order': 96, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.a1', '4.f1'], 'contains': ['16.b1', '16.c1', '24.f1'], 'core': '16.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2184, -1, 4094, -1], 'generators': [2, 48, 32], 'label': '96.219.8.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.f1', 'projective_image': '48.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000329
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1152, 'centralizer': '2.b1', 'complements': ['8.g1'], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '6.a1', '6.b1'], 'contains': ['24.a1', '24.b1', '24.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5024, 4900, 6296, 6713], 'generators': [2, 8, 48], 'label': '96.219.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000330
    {'ambient': '96.219', 'aut_centralizer_order': 384, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 384, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.a1', '6.c1', '6.d1'], 'contains': ['24.a1', '24.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3325, 2343, 3360, 9459], 'generators': [1, 8, 48], 'label': '96.219.12.b1', 'mobius_quo': -8, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.a1', '24.c1'], 'normalizer': '1.a1', 'old_label': '12.b1', '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.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000331
    {'ambient': '96.219', 'aut_centralizer_order': 64, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1152, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '6.b1', '6.c1'], 'contains': ['24.a1', '24.d1', '24.g1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5863, -1, 4828, -1], 'generators': [6, 8, 48], 'label': '96.219.12.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.c1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000332
    {'ambient': '96.219', 'aut_centralizer_order': 64, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1152, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '6.b1', '6.d1'], 'contains': ['24.a1', '24.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8477, -1, 7515, -1], 'generators': [4, 48], 'label': '96.219.12.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.d1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000333
    {'ambient': '96.219', 'aut_centralizer_order': 48, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2304, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.e1', '6.b1'], 'contains': ['24.b1', '24.d1', '24.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9453, -1, 9131, -1], 'generators': [2, 84], 'label': '96.219.12.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60000334
    {'ambient': '96.219', 'aut_centralizer_order': 24, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20089', 'aut_weyl_index': 24, 'centralizer': '2.b1', 'complements': ['48.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.f1', '6.a1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2802, 3338, 3758, 8413], 'generators': [1, 32, 2, 8, 48], 'label': '96.219.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', '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', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000335
    {'ambient': '96.219', 'aut_centralizer_order': 48, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 384, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '6.a1'], 'contains': ['24.c1', '24.f1'], 'core': '24.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [932, -1, 2323, -1], 'generators': [1, 2, 48], 'label': '96.219.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.f1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000336
    {'ambient': '96.219', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 384, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '6.c1'], 'contains': ['24.c1', '24.g1'], 'core': '24.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [1516, -1, 855, -1], 'generators': [1, 6, 48], 'label': '96.219.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.g1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000337
    {'ambient': '96.219', 'aut_centralizer_order': 4608, 'aut_label': '16.a1', 'aut_quo_index': 210, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '48.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7363, 6033, 7118, 3678], 'generators': [8, 32], 'label': '96.219.16.a1', 'mobius_quo': 1, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '48.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000338
    {'ambient': '96.219', 'aut_centralizer_order': 768, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': ['6.b1'], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.e1', '8.f1', '8.g1'], 'contains': ['32.a1', '48.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3263, 2972, 4007, 5655], 'generators': [48, 32], 'label': '96.219.16.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.e1'], 'normal_contains': ['32.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '48.43', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000339
    {'ambient': '96.219', 'aut_centralizer_order': 576, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.f1'], 'contains': ['32.a1', '48.c1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4543, -1, 6081, -1], 'generators': [50, 32], 'label': '96.219.16.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.c1', 'projective_image': '96.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000340
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1536, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.g1'], 'contains': ['32.a1', '48.d1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6083, -1, 5044, -1], 'generators': [86, 32], 'label': '96.219.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.d1', 'projective_image': '96.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60000341
    {'ambient': '96.219', 'aut_centralizer_order': 1536, 'aut_label': '24.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.c1', '12.d1'], 'contains': ['48.a1', '48.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5382, 4206, 5562, 6625], 'generators': [8, 48], 'label': '96.219.24.a1', 'mobius_quo': 2, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1'], 'normal_contains': ['48.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000342
    {'ambient': '96.219', 'aut_centralizer_order': 1152, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': ['4.g1'], 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '12.a1', '12.e1'], 'contains': ['48.a1', '48.c1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6840, 6196, 7636, 4685], 'generators': [50, 8], 'label': '96.219.24.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.b1', '12.a1'], 'normal_contains': ['48.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000343
    {'ambient': '96.219', 'aut_centralizer_order': 384, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1', 'complements': ['4.e1'], 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '12.b1', '12.f1', '12.g1'], 'contains': ['48.b1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1165, 2217, 2323, 8086], 'generators': [1, 48], 'label': '96.219.24.c1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.e1', '12.b1'], 'normal_contains': ['48.b1'], 'normalizer': '1.a1', 'old_label': '24.c1', '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', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000344
    {'ambient': '96.219', 'aut_centralizer_order': 384, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '12.c1', '12.e1'], 'contains': ['48.a1', '48.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7775, -1, 6599, -1], 'generators': [86, 8], 'label': '96.219.24.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.d1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000345
    {'ambient': '96.219', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157664', 'aut_weyl_index': 8, 'centralizer': '12.b1', 'complements': ['48.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.g1', '6.c1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3882, 5315, 2700, 4068], 'generators': [1, 32, 6, 8, 48], 'label': '96.219.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', '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', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000346
    {'ambient': '96.219', 'aut_centralizer_order': 384, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '12.d1', '12.e1'], 'contains': ['48.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8965, -1, 8640, -1], 'generators': [84], 'label': '96.219.24.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.e1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000347
    {'ambient': '96.219', 'aut_centralizer_order': 192, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.f1', '12.a1', '12.f1'], 'contains': ['48.b1', '48.c1'], 'core': '48.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2837, -1, 4525, -1], 'generators': [2, 48], 'label': '96.219.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.f1', 'projective_image': '48.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000348
    {'ambient': '96.219', 'aut_centralizer_order': 64, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.g1', '12.c1', '12.g1'], 'contains': ['48.b1', '48.d1'], 'core': '48.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3772, -1, 3488, -1], 'generators': [6, 48], 'label': '96.219.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '24.g1', 'projective_image': '48.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000349
    {'ambient': '96.219', 'aut_centralizer_order': 4608, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'contains': ['96.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5546, 4232, 5569, 3803], 'generators': [32], 'label': '96.219.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['96.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '96.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000350
    {'ambient': '96.219', 'aut_centralizer_order': 9216, 'aut_label': '48.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.d1', '24.e1'], 'contains': ['96.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7101, 5202, 6855, 4710], 'generators': [8], 'label': '96.219.48.a1', 'mobius_quo': -1, 'mobius_sub': -192, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1', '24.b1'], 'normal_contains': ['96.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '48.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.51', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000351
    {'ambient': '96.219', 'aut_centralizer_order': 1536, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': ['2.a1'], 'conjugacy_class_count': 6, 'contained_in': ['16.b1', '24.a1', '24.c1', '24.f1', '24.g1'], 'contains': ['96.a1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3491, 3212, 4269, 6133], 'generators': [48], 'label': '96.219.48.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.b1', '24.a1', '24.c1'], 'normal_contains': ['96.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '48.43', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.43', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000352
    {'ambient': '96.219', 'aut_centralizer_order': 1152, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 9216, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '24.b1', '24.f1'], 'contains': ['96.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4859, -1, 6067, -1], 'generators': [50], 'label': '96.219.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.c1', 'projective_image': '96.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000353
    {'ambient': '96.219', 'aut_centralizer_order': 384, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 9216, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '24.d1', '24.g1'], 'contains': ['96.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5939, -1, 5051, -1], 'generators': [86], 'label': '96.219.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '48.d1', 'projective_image': '96.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000354
    {'ambient': '96.219', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1', '48.d1'], 'contains': [], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5546, 4232, 5569, 4710], 'generators': [], 'label': '96.219.96.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1', '48.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '96.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60000355
    {'ambient': '96.219', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157664', 'aut_weyl_index': 8, 'centralizer': '12.b1', 'complements': ['48.c1', '48.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '6.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5801, 1158, 5986, 6234], 'generators': [1, 32, 4, 48, 8], 'label': '96.219.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.d1', '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.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000356
    {'ambient': '96.219', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1536.408640869', 'aut_weyl_index': 6, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4810, -1, 4822, -1], 'generators': [1, 2, 4, 48], 'label': '96.219.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.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', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60000357
    {'ambient': '96.219', 'aut_centralizer_order': 96, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 576, 'centralizer': '2.b1', 'complements': ['24.g1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.f1', '12.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4845, 5719, 6862, 6108], 'generators': [2, 8, 48, 32], 'label': '96.219.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60000358
    {'ambient': '96.219', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 192, 'centralizer': '12.b1', 'complements': ['24.f1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.a1', '8.c1', '8.g1', '12.c1'], 'core': '4.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6716, 7695, 4747, 2028], 'generators': [6, 8, 48, 32], 'label': '96.219.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.a1', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60000359
    {'ambient': '96.219', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 192, 'centralizer': '12.b1', 'complements': ['24.f1', '24.g1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '8.d1', '12.d1'], 'core': '4.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [8345, 3677, 8876, 4068], 'generators': [4, 48, 8, 32], 'label': '96.219.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}