Abstract group data - 336.138

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 14, 6, 2, 14, 14], 'aut_gens': [[1, 2, 4], [289, 114, 164], [49, 58, 116], [13, 58, 92], [181, 58, 332], [49, 2, 284], [217, 2, 172]], 'aut_group': None, 'aut_hash': 866793471638122205, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4032, 'aut_permdeg': 34, 'aut_perms': [116923022854221076043432069544214640846, 134324194420506388227589737726143404320, 291737902755339010188846428936840665700, 99186605002917359344622378583306328256, 134222667538959708351485726997022029136, 251952237590518858298336108366933831624], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 14, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 3, 2, 1], [4, 42, 2, 1], [6, 2, 1, 1], [6, 28, 2, 1], [7, 2, 3, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 6, 6, 1], [21, 4, 3, 1], [28, 2, 6, 1], [28, 6, 6, 1], [42, 4, 3, 1], [84, 4, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^4\\times C_6)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 14, 2], [3, 2, 1], [4, 2, 1], [4, 3, 2], [4, 42, 2], [6, 2, 1], [6, 28, 2], [7, 2, 3], [12, 4, 1], [14, 2, 3], [14, 6, 6], [21, 4, 3], [28, 2, 6], [28, 6, 6], [42, 4, 3], [84, 4, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 138, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 14, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 3, 2, 1], [4, 42, 1, 2], [6, 2, 1, 1], [6, 28, 1, 2], [7, 2, 3, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 6, 6, 1], [21, 4, 3, 1], [28, 2, 6, 1], [28, 6, 6, 1], [42, 4, 3, 1], [84, 4, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2688, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, -1, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '168.50', 'hash': 138, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 42], 'inner_gens': [[1, 2, 220], [1, 2, 116], [121, 226, 4]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 24, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 30], [4, 13]], 'label': '336.138', 'linC_count': 54, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 12, 'linQ_dim_count': 16, 'linR_count': 24, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D28:S3', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 51, 'number_divisions': 22, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 80, 'number_subgroups': 420, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 35], [3, 2], [4, 92], [6, 58], [7, 6], [12, 4], [14, 42], [21, 12], [28, 48], [42, 12], [84, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 170, 4], [1, 2, 172], [85, 2, 76]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [40320, 24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 2], [6, 4], [12, 2], [24, 2]], 'representations': {'PC': {'code': 8123140261482178403927116044919884683, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -7, 1015, 3962, 1052, 50, 2499, 2793, 69, 6244, 1930, 118, 10373]}, 'GLZN': {'d': 2, 'p': 58, 'gens': [195575, 2440594, 5952599, 11121441, 4489949, 2692057]}, 'Perm': {'d': 18, 'gens': [5337514828927, 400335207189120, 777033521510400, 1156002822374400, 403200, 973]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{28}:S_3', 'transitive_degree': 168, '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: 109826126
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 138, 'group_order': 336, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109826137
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 138, 'group_order': 336, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 168, 'size': 1}
  • id: 109826148
    {'aut_label': '2B', 'centralizer': '6.c1.a1', 'counter': 3, 'group_counter': 138, 'group_order': 336, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 198, 'size': 6}
  • id: 109826159
    {'aut_label': '2C', 'centralizer': '14.c1.a1', 'counter': 4, 'group_counter': 138, 'group_order': 336, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 73, 'size': 14}
  • id: 109826170
    {'aut_label': '2C', 'centralizer': '14.c1.b1', 'counter': 5, 'group_counter': 138, 'group_order': 336, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 85, 'size': 14}
  • id: 109826173
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 6, 'group_counter': 138, 'group_order': 336, 'label': '3A', 'order': 3, 'powers': [6, 1, 6], 'representative': 112, 'size': 2}
  • id: 109826174
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 7, 'group_counter': 138, 'group_order': 336, 'label': '4A', 'order': 4, 'powers': [2, 7, 7], 'representative': 84, 'size': 2}
  • id: 109826175
    {'aut_label': '4B1', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 138, 'group_order': 336, 'label': '4B1', 'order': 4, 'powers': [2, 9, 9], 'representative': 170, 'size': 3}
  • id: 109826176
    {'aut_label': '4B1', 'centralizer': '3.a1.a1', 'counter': 9, 'group_counter': 138, 'group_order': 336, 'label': '4B-1', 'order': 4, 'powers': [2, 8, 8], 'representative': 2, 'size': 3}
  • id: 109826127
    {'aut_label': '4C', 'centralizer': '42.c1.a1', 'counter': 10, 'group_counter': 138, 'group_order': 336, 'label': '4C', 'order': 4, 'powers': [2, 10, 10], 'representative': 307, 'size': 42}
  • id: 109826128
    {'aut_label': '4C', 'centralizer': '42.c1.b1', 'counter': 11, 'group_counter': 138, 'group_order': 336, 'label': '4D', 'order': 4, 'powers': [2, 11, 11], 'representative': 231, 'size': 42}
  • id: 109826129
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 12, 'group_counter': 138, 'group_order': 336, 'label': '6A', 'order': 6, 'powers': [6, 2, 12], 'representative': 56, 'size': 2}
  • id: 109826130
    {'aut_label': '6B', 'centralizer': '28.d1.a1', 'counter': 13, 'group_counter': 138, 'group_order': 336, 'label': '6B', 'order': 6, 'powers': [6, 4, 13], 'representative': 185, 'size': 28}
  • id: 109826131
    {'aut_label': '6B', 'centralizer': '28.d1.b1', 'counter': 14, 'group_counter': 138, 'group_order': 336, 'label': '6C', 'order': 6, 'powers': [6, 5, 14], 'representative': 197, 'size': 28}
  • id: 109826132
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 138, 'group_order': 336, 'label': '7A1', 'order': 7, 'powers': [16, 17, 1], 'representative': 288, 'size': 2}
  • id: 109826133
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 138, 'group_order': 336, 'label': '7A2', 'order': 7, 'powers': [17, 15, 1], 'representative': 240, 'size': 2}
  • id: 109826134
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 138, 'group_order': 336, 'label': '7A3', 'order': 7, 'powers': [15, 16, 1], 'representative': 192, 'size': 2}
  • id: 109826135
    {'aut_label': '12A', 'centralizer': '4.c1.a1', 'counter': 18, 'group_counter': 138, 'group_order': 336, 'label': '12A', 'order': 12, 'powers': [12, 7, 18], 'representative': 28, 'size': 4}
  • id: 109826136
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 138, 'group_order': 336, 'label': '14A1', 'order': 14, 'powers': [17, 20, 2], 'representative': 264, 'size': 2}
  • id: 109826138
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 138, 'group_order': 336, 'label': '14A3', 'order': 14, 'powers': [16, 21, 2], 'representative': 120, 'size': 2}
  • id: 109826139
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 138, 'group_order': 336, 'label': '14A5', 'order': 14, 'powers': [15, 19, 2], 'representative': 312, 'size': 2}
  • id: 109826140
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 22, 'group_counter': 138, 'group_order': 336, 'label': '14B1', 'order': 14, 'powers': [15, 24, 3], 'representative': 6, 'size': 6}
  • id: 109826141
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 23, 'group_counter': 138, 'group_order': 336, 'label': '14B-1', 'order': 14, 'powers': [15, 25, 3], 'representative': 54, 'size': 6}
  • id: 109826142
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 24, 'group_counter': 138, 'group_order': 336, 'label': '14B3', 'order': 14, 'powers': [17, 27, 3], 'representative': 294, 'size': 6}
  • id: 109826143
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 25, 'group_counter': 138, 'group_order': 336, 'label': '14B-3', 'order': 14, 'powers': [17, 26, 3], 'representative': 14, 'size': 6}
  • id: 109826144
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 26, 'group_counter': 138, 'group_order': 336, 'label': '14B5', 'order': 14, 'powers': [16, 22, 3], 'representative': 22, 'size': 6}
  • id: 109826145
    {'aut_label': '14B1', 'centralizer': '6.c1.a1', 'counter': 27, 'group_counter': 138, 'group_order': 336, 'label': '14B-5', 'order': 14, 'powers': [16, 23, 3], 'representative': 38, 'size': 6}
  • id: 109826146
    {'aut_label': '21A1', 'centralizer': '4.c1.a1', 'counter': 28, 'group_counter': 138, 'group_order': 336, 'label': '21A1', 'order': 21, 'powers': [29, 15, 6], 'representative': 16, 'size': 4}
  • id: 109826147
    {'aut_label': '21A1', 'centralizer': '4.c1.a1', 'counter': 29, 'group_counter': 138, 'group_order': 336, 'label': '21A2', 'order': 21, 'powers': [30, 16, 6], 'representative': 32, 'size': 4}
  • id: 109826149
    {'aut_label': '21A1', 'centralizer': '4.c1.a1', 'counter': 30, 'group_counter': 138, 'group_order': 336, 'label': '21A4', 'order': 21, 'powers': [28, 17, 6], 'representative': 64, 'size': 4}
  • id: 109826150
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 31, 'group_counter': 138, 'group_order': 336, 'label': '28A1', 'order': 28, 'powers': [21, 32, 7], 'representative': 12, 'size': 2}
  • id: 109826151
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 138, 'group_order': 336, 'label': '28A3', 'order': 28, 'powers': [19, 34, 7], 'representative': 36, 'size': 2}
  • id: 109826152
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 138, 'group_order': 336, 'label': '28A5', 'order': 28, 'powers': [20, 36, 7], 'representative': 60, 'size': 2}
  • id: 109826153
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 138, 'group_order': 336, 'label': '28A9', 'order': 28, 'powers': [20, 31, 7], 'representative': 108, 'size': 2}
  • id: 109826154
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 138, 'group_order': 336, 'label': '28A11', 'order': 28, 'powers': [19, 33, 7], 'representative': 132, 'size': 2}
  • id: 109826155
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 138, 'group_order': 336, 'label': '28A13', 'order': 28, 'powers': [21, 35, 7], 'representative': 156, 'size': 2}
  • id: 109826156
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 37, 'group_counter': 138, 'group_order': 336, 'label': '28B1', 'order': 28, 'powers': [19, 39, 8], 'representative': 50, 'size': 6}
  • id: 109826157
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 38, 'group_counter': 138, 'group_order': 336, 'label': '28B-1', 'order': 28, 'powers': [19, 40, 9], 'representative': 10, 'size': 6}
  • id: 109826158
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 39, 'group_counter': 138, 'group_order': 336, 'label': '28B3', 'order': 28, 'powers': [20, 41, 9], 'representative': 26, 'size': 6}
  • id: 109826160
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 40, 'group_counter': 138, 'group_order': 336, 'label': '28B-3', 'order': 28, 'powers': [20, 42, 8], 'representative': 34, 'size': 6}
  • id: 109826161
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 41, 'group_counter': 138, 'group_order': 336, 'label': '28B5', 'order': 28, 'powers': [21, 38, 8], 'representative': 18, 'size': 6}
  • id: 109826162
    {'aut_label': '28B1', 'centralizer': '6.c1.a1', 'counter': 42, 'group_counter': 138, 'group_order': 336, 'label': '28B-5', 'order': 28, 'powers': [21, 37, 9], 'representative': 42, 'size': 6}
  • id: 109826163
    {'aut_label': '42A1', 'centralizer': '4.c1.a1', 'counter': 43, 'group_counter': 138, 'group_order': 336, 'label': '42A1', 'order': 42, 'powers': [28, 21, 12], 'representative': 8, 'size': 4}
  • id: 109826164
    {'aut_label': '42A1', 'centralizer': '4.c1.a1', 'counter': 44, 'group_counter': 138, 'group_order': 336, 'label': '42A5', 'order': 42, 'powers': [29, 20, 12], 'representative': 40, 'size': 4}
  • id: 109826165
    {'aut_label': '42A1', 'centralizer': '4.c1.a1', 'counter': 45, 'group_counter': 138, 'group_order': 336, 'label': '42A11', 'order': 42, 'powers': [30, 19, 12], 'representative': 88, 'size': 4}
  • id: 109826166
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 46, 'group_counter': 138, 'group_order': 336, 'label': '84A1', 'order': 84, 'powers': [43, 31, 18], 'representative': 4, 'size': 4}
  • id: 109826167
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 47, 'group_counter': 138, 'group_order': 336, 'label': '84A5', 'order': 84, 'powers': [44, 33, 18], 'representative': 20, 'size': 4}
  • id: 109826168
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 48, 'group_counter': 138, 'group_order': 336, 'label': '84A11', 'order': 84, 'powers': [45, 35, 18], 'representative': 292, 'size': 4}
  • id: 109826169
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 49, 'group_counter': 138, 'group_order': 336, 'label': '84A13', 'order': 84, 'powers': [43, 36, 18], 'representative': 52, 'size': 4}
  • id: 109826171
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 50, 'group_counter': 138, 'group_order': 336, 'label': '84A19', 'order': 84, 'powers': [44, 34, 18], 'representative': 148, 'size': 4}
  • id: 109826172
    {'aut_label': '84A1', 'centralizer': '4.c1.a1', 'counter': 51, 'group_counter': 138, 'group_order': 336, 'label': '84A25', 'order': 84, 'powers': [45, 32, 18], 'representative': 100, 'size': 4}
• gps_qchar •

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

  
  
  • id: 4411188
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411199
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411203
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411204
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411205
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411206
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411207
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411208
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411209
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, -1, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411189
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, -2, -1, 2, 0, 0, 0, 0, -1, 1, 1, 2, 2, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411190
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 2, -1, -2, 0, 0, 0, 0, -1, 1, -1, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411191
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -2, -1, -2, 0, 0, 0, 0, -1, -1, 1, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411192
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, 4, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4411198
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.4a', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 4, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4411193
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2f', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 6, 6, 6, 6, 0, 0, 6, 0, 0, -1, -1, -1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4411194
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2g', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 6, -6, 6, 6, 0, 0, 6, 0, 0, -1, -1, -1, -6, -1, -1, -1, 1, 1, 1, 1, 1, 1, -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: 4411195
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2h', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 6, 6, -6, -6, 0, 0, 6, 0, 0, -1, -1, -1, 6, -1, -1, -1, 1, 1, 1, 1, 1, 1, -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: 4411196
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2i', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 6, -6, -6, -6, 0, 0, 6, 0, 0, -1, -1, -1, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4411200
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.4b', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, -6, 12, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, -6, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4411201
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.4c', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, -6, -12, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, 6, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4411197
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.2j', 'multiplicity': 12, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 24, 0, 0, 0, 0, 0, -24, 0, 0, -4, -4, -4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4411202
    {'cdim': 4, 'counter': 22, 'faithful': True, 'group': '336.138', 'group_order': 336, 'image': None, 'label': '336.138.4d', 'multiplicity': 6, 'nt': [168, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, -12, 0, 0, 0, 0, 0, 12, 0, 0, -4, -4, -4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• 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: 6733764
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 336, 'label': '336.138.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733775
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 168, 'label': '336.138.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733786
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 168, 'label': '336.138.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733797
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 168, 'label': '336.138.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733808
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 168, 'label': '336.138.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733811
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 168, 'label': '336.138.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733812
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 168, 'label': '336.138.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733813
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 336, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 168, 'label': '336.138.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733814
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 56, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 56, 'label': '336.138.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733765
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 56, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 28, 'label': '336.138.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6733766
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 56, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 28, 'label': '336.138.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733767
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 56, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 28, 'label': '336.138.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6733768
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 84, 'counter': 13, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 21, 'label': '336.138.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6733769
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 84, 'counter': 14, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 21, 'label': '336.138.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6733770
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 15, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 24, 'label': '336.138.2f1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 6733771
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 16, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 24, 'label': '336.138.2f2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 6733772
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 17, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 24, 'label': '336.138.2f3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733773
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 18, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 12, 'label': '336.138.2g1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733774
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 19, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 12, 'label': '336.138.2g2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 6733776
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 20, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 12, 'label': '336.138.2g3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733777
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 21, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 12, 'label': '336.138.2h1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 6733778
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 22, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 12, 'label': '336.138.2h2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 6733779
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 23, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 12, 'label': '336.138.2h3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733780
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 24, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 12, 'label': '336.138.2i1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733781
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 12, 'label': '336.138.2i2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 6733782
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 12, 'label': '336.138.2i3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733783
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 27, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j1', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, 8]], [[-1, 4], [-1, 10]], [[1, 6], [1, 8]], [[1, 4], [1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, 9]], [[1, 3], [1, 11]], [[1, 5], [1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [-1, 11]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 6733793
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 36, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j10', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, 8]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[1, 6], [1, 8]], [[-1, 4], [-1, 10]], [[1, 4], [1, 10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, 11]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 3], [1, 11]], [[1, 5], [1, 9]], [[-1, 5], [-1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 6733794
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 37, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j11', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, 8]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[1, 6], [1, 8]], [[-1, 4], [-1, 10]], [[1, 4], [1, 10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 3], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 5], [1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733795
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 38, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j12', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[1, 6], [1, 8]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, 8]], [[1, 4], [1, 10]], [[-1, 4], [-1, 10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, 11]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 3], [1, 11]], [[1, 5], [1, 9]], [[-1, 5], [-1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733784
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 28, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j2', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, 8]], [[1, 4], [1, 10]], [[-1, 6], [-1, 8]], [[-1, 4], [-1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, 9]], [[-1, 3], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 3], [1, 11]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 6733785
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 29, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j3', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, 8]], [[1, 4], [1, 10]], [[-1, 6], [-1, 8]], [[-1, 4], [-1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, 9]], [[1, 3], [1, 11]], [[1, 5], [1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [-1, 11]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 6733787
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 30, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j4', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, 8]], [[-1, 4], [-1, 10]], [[1, 6], [1, 8]], [[1, 4], [1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, 9]], [[-1, 3], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 3], [1, 11]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 6733788
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 31, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j5', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 4], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 6], [-1, 8]], [[1, 6], [1, 8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 3], [1, 11]], [[-1, 3], [-1, 11]], [[1, 5], [1, 9]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733789
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 32, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j6', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 4], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 6], [1, 8]], [[-1, 6], [-1, 8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 5], [1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 3], [-1, 11]], [[1, 3], [1, 11]], [[-1, 5], [-1, 9]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733790
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 33, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j7', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 4], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 6], [1, 8]], [[-1, 6], [-1, 8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 3], [1, 11]], [[-1, 3], [-1, 11]], [[1, 5], [1, 9]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733791
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 34, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j8', 'nt': [56, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 7]], [[-2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[1, 4], [1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[-1, 6], [-1, 8]], [[1, 6], [1, 8]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 5], [1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 3], [-1, 11]], [[1, 3], [1, 11]], [[-1, 5], [-1, 9]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733792
    {'center': '28.c1.a1', 'center_index': 28, 'center_order': 12, 'counter': 35, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '112.30', 'image_order': 112, 'indicator': 0, 'kernel': '112.a1.a1', 'kernel_order': 3, 'label': '336.138.2j9', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 0], [-2, 2], [1, 4], [-1, 6], [1, 8], [-1, 10]], [[1, 6], [1, 8]], [[-1, 0], [2, 2], [-1, 4], [1, 6], [-1, 8], [1, 10]], [[-1, 6], [-1, 8]], [[1, 4], [1, 10]], [[-1, 4], [-1, 10]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 3], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 5], [1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 6733796
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 14, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.a1.a1', 'kernel_order': 7, 'label': '336.138.4a', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6733798
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 4, 'label': '336.138.4b1', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733799
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 4, 'label': '336.138.4b2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 6733800
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 42, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 4, 'label': '336.138.4b3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733801
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 43, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 2, 'label': '336.138.4c1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 6733802
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 2, 'label': '336.138.4c2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 6733803
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 2, 'label': '336.138.4c3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733804
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 46, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d1', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 6733805
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 47, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d2', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 6733806
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 48, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d3', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6733807
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 49, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d4', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 6733809
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 50, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d5', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 6733810
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 2, 'counter': 51, 'cyclotomic_n': 28, 'dim': 4, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '336.138', 'group_counter': 138, 'group_order': 336, 'image': None, 'image_isoclass': '336.138', 'image_order': 336, 'indicator': -1, 'kernel': '336.a1.a1', 'kernel_order': 1, 'label': '336.138.4d6', 'nt': [168, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
• 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: 65538661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 336, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '336.138.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 65538672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 168, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 168, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 168, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65538740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '336.138.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 65538662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 84, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 84, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 84, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538665
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 84, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 65538666
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 84, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538667
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538668
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 56, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65538677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '336.138.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 65538678
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 42, 'counter': 25, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 65538679
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 21, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538680
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 21, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538681
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 21, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538685
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 28, 'counter': 31, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538687
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 65538688
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538689
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 24, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 65538691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65538698
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 21, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '336.138.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 65538699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '336.138.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 65538700
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 14, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538701
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 7, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 65538702
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538703
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 65538704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 65538706
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 12, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 65538707
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': True, 'centralizer_order': 56, 'characteristic': True, 'core_order': 12, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '336.138.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 65538708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 65538709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 65538710
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538711
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 65538719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 65538720
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 7, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '336.138.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 65538721
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 6, 'counter': 64, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 65538722
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 65538723
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 65538724
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.56.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 65538725
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 4, 'counter': 68, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 65538726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '336.138.84.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538730
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538731
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538732
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.84.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 65538733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 3, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '336.138.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 65538734
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': True, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '336.138.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 65538735
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 65538736
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 65538737
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '336.138.168.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 65538739
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '336.138', 'ambient_counter': 138, 'ambient_order': 336, 'ambient_tex': 'D_{28}:S_3', 'central': True, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '336.138.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '336.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}:S_3', '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: 65538661
    {'ambient': '336.138', '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': '168.a1.a1', 'complements': ['336.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3048, 4772, 6032, 5234, 5091, 6098, 3978, 4683], 'generators': [1, 48, 84, 168, 2, 112], 'label': '336.138.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538662
    {'ambient': '336.138', 'aut_centralizer_order': 56, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '72.48', 'aut_weyl_index': 56, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '12.c1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7923, 965, 1728, 2385, 365, 4082, 763, 8175], 'generators': [198, 48, 112, 168], 'label': '336.138.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538663
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.a1.a1', '28.d1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7017, 8004, 2263, 5065, 1125, 7973, 217, 1306], 'generators': [1, 112, 48, 168], 'label': '336.138.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 65538664
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.b1', '12.a1.b1', '28.d1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7017, 8004, 2889, 7615, 1125, 7973, 1309, 2511], 'generators': [181, 112, 48, 168], 'label': '336.138.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 65538665
    {'ambient': '336.138', 'aut_centralizer_order': 168, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 168, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '28.b1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4860, 6488, 7311, 8740, 5147, 5444, 5543, 4551], 'generators': [84, 48, 168, 112], 'label': '336.138.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538666
    {'ambient': '336.138', 'aut_centralizer_order': 56, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '72.48', 'aut_weyl_index': 56, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.a1.a1', '12.d1.a1', '28.c1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3297, 3178, 6396, 742, 2969, 2283, 4578, 6724], 'generators': [2, 168, 112, 48], 'label': '336.138.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.a1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538667
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.e1.a1', '28.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1325, 5094, 3914, 6339, 2244, 6578, 5922, 5466], 'generators': [3, 112, 48, 168], 'label': '336.138.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538668
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.e1.b1', '28.e1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1325, 5094, 9791, 3790, 2244, 6578, 2965, 3637], 'generators': [295, 112, 48, 168], 'label': '336.138.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538687
    {'ambient': '336.138', 'aut_centralizer_order': 112, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 336, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '84.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3175, -1, 8190, -1, 7087, -1, 3971, -1], 'generators': [2, 168, 48], 'label': '336.138.12.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538669
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 12, 'centralizer': '28.c1.a1', 'complements': ['56.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '42.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5639, 9035, 6385, 8103, 8885, 9204, 2154, 312], 'generators': [1, 168, 48, 84], 'label': '336.138.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538670
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.e1.b1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6598, -1, 4907, -1, 6839, -1, 1775, -1], 'generators': [1, 168, 48, 198], 'label': '336.138.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538671
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.c1.a1', '12.e1.a1', '42.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6598, -1, 4074, -1, 6839, -1, 2532, -1], 'generators': [181, 168, 48, 198], 'label': '336.138.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538672
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['168.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.b1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6179, 2856, 3509, 2147, 1976, 7657, 1786, 3637], 'generators': [1, 168, 112, 198, 48], 'label': '336.138.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538673
    {'ambient': '336.138', 'aut_centralizer_order': 56, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.15', 'aut_weyl_index': 168, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '42.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4161, -1, 8404, -1, 8247, -1, 3978, -1], 'generators': [2, 48, 168, 84], 'label': '336.138.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538674
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '42.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2756, -1, 7378, -1, 7487, -1, 5132, -1], 'generators': [1, 168, 48, 2], 'label': '336.138.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538675
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 24, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.d1.a1', '12.e1.b1', '42.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2756, -1, 8937, -1, 7487, -1, 3432, -1], 'generators': [181, 168, 48, 2], 'label': '336.138.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538676
    {'ambient': '336.138', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.125', 'aut_weyl_index': 12, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.e1.b1', '42.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2146, -1, 9351, -1, 9813, -1, 6308, -1], 'generators': [3, 168, 48, 84], 'label': '336.138.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538677
    {'ambient': '336.138', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.209', 'aut_weyl_index': 42, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.b1.b1', '14.c1.a1', '14.c1.b1', '14.d1.a1', '14.e1.a1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [943, -1, 6228, -1, 5740, -1, 7954, -1], 'generators': [1, 112, 2, 84, 168], 'label': '336.138.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 65538678
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 336, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '24.a1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6514, 5014, 2643, 4686, 2462, 5444, 3315, 4551], 'generators': [168, 48, 112], 'label': '336.138.8.a1.a1', 'mobius_quo': -1, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.e1.b1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538679
    {'ambient': '336.138', 'aut_centralizer_order': 56, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 112, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '56.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9804, -1, 209, -1, 836, -1, 1167, -1], 'generators': [198, 112, 48], 'label': '336.138.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65538680
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '56.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8994, -1, 1180, -1, 1525, -1, 672, -1], 'generators': [1, 48, 112], 'label': '336.138.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538681
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.a1', '24.c1.b1', '56.c1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8994, -1, 692, -1, 1525, -1, 1662, -1], 'generators': [181, 48, 112], 'label': '336.138.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.c1.b1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538682
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '28.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '84.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7325, 9035, 4473, 6330, 5806, 7973, 2074, 1306], 'generators': [1, 48, 168], 'label': '336.138.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538683
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['168.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.e1.a1', '6.b1.b1', '14.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6179, 2856, 3031, 6658, 1976, 7657, 2885, 7199], 'generators': [181, 168, 112, 198, 48], 'label': '336.138.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538684
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '28.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.b1.b1', '6.d1.b1'], 'contains': ['24.a1.a1', '24.c1.b1', '84.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7325, 9035, 4157, 7216, 5806, 7973, 2991, 2511], 'generators': [181, 48, 168], 'label': '336.138.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538685
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 336, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '84.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4680, 7843, 8617, 8103, 8911, 6708, 4291, 3777], 'generators': [84, 168, 48], 'label': '336.138.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538686
    {'ambient': '336.138', 'aut_centralizer_order': 112, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 336, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '84.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7992, -1, 3569, -1, 5167, -1, 2532, -1], 'generators': [198, 48, 168], 'label': '336.138.12.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538688
    {'ambient': '336.138', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.b1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '84.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2497, -1, 6189, -1, 6631, -1, 4619, -1], 'generators': [3, 48, 168], 'label': '336.138.12.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538689
    {'ambient': '336.138', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 48, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.b1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '84.e1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2497, -1, 9389, -1, 6631, -1, 3643, -1], 'generators': [295, 48, 168], 'label': '336.138.12.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 65538690
    {'ambient': '336.138', 'aut_centralizer_order': 168, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 168, 'centralizer': '12.b1.a1', 'complements': ['24.c1.a1', '24.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.b1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3015, 1984, 6655, 2436, 4580, 638, 8842, 9485], 'generators': [2, 84, 168, 112], 'label': '336.138.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538691
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.a1', '28.e1.b1', '42.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5432, -1, 3618, -1, 1707, -1, 6643, -1], 'generators': [1, 198, 168, 112], 'label': '336.138.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 65538692
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.b1', '28.e1.a1', '42.a1.b1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5432, -1, 2814, -1, 1707, -1, 7480, -1], 'generators': [181, 198, 168, 112], 'label': '336.138.14.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 65538693
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 168, 'centralizer': '84.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.d1.a1', '28.e1.a1', '42.c1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1082, -1, 4836, -1, 3814, -1, 9392, -1], 'generators': [1, 2, 168, 112], 'label': '336.138.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538694
    {'ambient': '336.138', 'aut_centralizer_order': 28, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.195', 'aut_weyl_index': 28, 'centralizer': '12.b1.a1', 'complements': ['168.c1.a1', '168.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.c1.a1', '14.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4033, 965, 6972, 742, 4265, 3003, 4531, 8438], 'generators': [2, 48, 168, 84, 112], 'label': '336.138.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538695
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 168, 'centralizer': '84.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.d1.b1', '28.e1.b1', '42.c1.b1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1082, -1, 7734, -1, 3814, -1, 7954, -1], 'generators': [181, 2, 168, 112], 'label': '336.138.14.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538696
    {'ambient': '336.138', 'aut_centralizer_order': 36, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 252, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.d1.a1', '28.d1.b1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4621, -1, 5378, -1, 5719, -1, 7062, -1], 'generators': [1, 84, 112, 168], 'label': '336.138.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 65538697
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.38', 'aut_weyl_index': 84, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.e1.a1', '28.e1.b1', '42.e1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [196, -1, 8196, -1, 6302, -1, 9865, -1], 'generators': [3, 84, 168, 112], 'label': '336.138.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 65538698
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '16.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 336, 'centralizer': '4.c1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1'], 'contains': ['48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8861, 5764, 706, 4059, 2320, 5161, 2248, 4551], 'generators': [112, 48], 'label': '336.138.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '336.138', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538699
    {'ambient': '336.138', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 252, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.a1.b1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.d1.a1', '42.e1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2008, -1, 8663, -1, 9346, -1, 8427, -1], 'generators': [1, 2, 84], 'label': '336.138.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538700
    {'ambient': '336.138', 'aut_centralizer_order': 672, 'aut_label': '24.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 672, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.e1.b1'], 'contains': ['48.a1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7521, 7843, 5171, 6619, 5785, 6905, 3938, 3777], 'generators': [168, 48], 'label': '336.138.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538701
    {'ambient': '336.138', 'aut_centralizer_order': 112, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 672, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '168.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9699, -1, 621, -1, 2766, -1, 2569, -1], 'generators': [198, 48], 'label': '336.138.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.b1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538702
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 96, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9249, -1, 1433, -1, 3536, -1, 1957, -1], 'generators': [1, 48], 'label': '336.138.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.c1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 65538703
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 96, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.a1.b1'], 'contains': ['48.a1.a1', '168.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9249, -1, 1042, -1, 3536, -1, 2860, -1], 'generators': [181, 48], 'label': '336.138.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.c1.b1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 65538704
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '28.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 336, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.b1.b1'], 'contains': ['56.a1.a1', '56.b1.a1', '84.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7091, 1930, 1981, 3321, 2057, 3613, 5412, 8175], 'generators': [198, 168, 112], 'label': '336.138.28.a1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538705
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['168.b1.a1', '168.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '6.d1.a1', '14.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2089, 4772, 4591, 5234, 3212, 6098, 5132, 5941], 'generators': [1, 168, 112, 2, 48], 'label': '336.138.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538706
    {'ambient': '336.138', 'aut_centralizer_order': 1008, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.a1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '84.a1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3980, 4746, 7400, 5314, 4529, 4485, 9141, 5607], 'generators': [84, 112, 168], 'label': '336.138.28.b1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.c1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538707
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '28.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 336, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.a1.a1', '14.c1.a1', '14.c1.b1'], 'contains': ['56.a1.a1', '84.d1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3101, 3030, 6267, 2296, 4073, 2283, 8318, 6724], 'generators': [2, 168, 112], 'label': '336.138.28.c1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.d1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65538708
    {'ambient': '336.138', 'aut_centralizer_order': 72, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.c1.a1', '84.c1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5846, -1, 2622, -1, 3029, -1, 5034, -1], 'generators': [1, 168, 112], 'label': '336.138.28.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538709
    {'ambient': '336.138', 'aut_centralizer_order': 72, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '28.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '14.b1.b1', '14.c1.b1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.c1.b1', '84.c1.b1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5846, -1, 3241, -1, 3029, -1, 5791, -1], 'generators': [181, 168, 112], 'label': '336.138.28.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538710
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 336, 'centralizer': '84.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.b1.b1', '14.c1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '84.e1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [774, -1, 3647, -1, 3607, -1, 9468, -1], 'generators': [3, 168, 112], 'label': '336.138.28.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538711
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 336, 'centralizer': '84.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '14.b1.a1', '14.c1.b1', '14.e1.a1'], 'contains': ['56.a1.a1', '84.e1.b1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [774, -1, 7737, -1, 3607, -1, 6993, -1], 'generators': [295, 168, 112], 'label': '336.138.28.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 65538712
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.a1', '84.e1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4956, -1, 5249, -1, 6216, -1, 6170, -1], 'generators': [1, 198], 'label': '336.138.42.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538713
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '14.b1.b1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.b1', '84.e1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4956, -1, 4356, -1, 6216, -1, 6694, -1], 'generators': [181, 198], 'label': '336.138.42.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538714
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.d1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2629, -1, 8585, -1, 8343, -1, 7903, -1], 'generators': [2, 84], 'label': '336.138.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538715
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '42.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1', '84.e1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1686, -1, 6880, -1, 7654, -1, 8733, -1], 'generators': [1, 2], 'label': '336.138.42.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538716
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['168.b1.a1', '168.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.d1.a1', '4.e1.b1', '6.d1.b1', '14.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2089, 4772, 8332, 3571, 3212, 6098, 3417, 2379], 'generators': [181, 168, 112, 2, 48], 'label': '336.138.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.d1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538717
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1008, 'centralizer': '42.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '14.c1.b1', '21.a1.a1'], 'contains': ['84.c1.b1', '84.d1.a1', '84.e1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1686, -1, 9069, -1, 7654, -1, 7408, -1], 'generators': [181, 2], 'label': '336.138.42.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538718
    {'ambient': '336.138', 'aut_centralizer_order': 72, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 504, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.c1.a1', '84.c1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4494, -1, 6097, -1, 9316, -1, 6432, -1], 'generators': [1, 84], 'label': '336.138.42.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538719
    {'ambient': '336.138', 'aut_centralizer_order': 24, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 504, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.e1.a1', '84.e1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1135, -1, 9574, -1, 9681, -1, 9767, -1], 'generators': [3, 84], 'label': '336.138.42.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 65538720
    {'ambient': '336.138', 'aut_centralizer_order': 672, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 672, 'centralizer': '2.b1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1'], 'contains': ['336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9222, 7856, 877, 6240, 3171, 6774, 2714, 4551], 'generators': [48], 'label': '336.138.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.138', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538721
    {'ambient': '336.138', 'aut_centralizer_order': 2016, 'aut_label': '56.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1'], 'contains': ['112.a1.a1', '168.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6058, 4102, 3281, 4577, 3900, 4289, 6712, 5888], 'generators': [168, 112], 'label': '336.138.56.a1.a1', 'mobius_quo': 1, 'mobius_sub': 56, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538722
    {'ambient': '336.138', 'aut_centralizer_order': 336, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 672, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '168.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8634, -1, 497, -1, 1915, -1, 3384, -1], 'generators': [198, 112], 'label': '336.138.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '56.b1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 65538723
    {'ambient': '336.138', 'aut_centralizer_order': 72, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '28.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.d1.a1'], 'contains': ['112.a1.a1', '168.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7949, -1, 1575, -1, 3171, -1, 3122, -1], 'generators': [1, 112], 'label': '336.138.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.c1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538724
    {'ambient': '336.138', 'aut_centralizer_order': 72, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '28.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '28.d1.b1'], 'contains': ['112.a1.a1', '168.c1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7949, -1, 934, -1, 3171, -1, 3647, -1], 'generators': [181, 112], 'label': '336.138.56.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.b1', 'old_label': '56.c1.b1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538725
    {'ambient': '336.138', 'aut_centralizer_order': 2016, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.b1.a1', '42.b1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3938, 6354, 7442, 5862, 8627, 6033, 7845, 5255], 'generators': [84], 'label': '336.138.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 42, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.b1.a1', '28.b1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '42.3', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538726
    {'ambient': '336.138', 'aut_centralizer_order': 672, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.a1.a1', '42.a1.a1', '42.a1.b1', '42.b1.a1'], 'contains': ['168.a1.a1', '168.b1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6461, -1, 3740, -1, 5258, -1, 6133, -1], 'generators': [198, 168], 'label': '336.138.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538727
    {'ambient': '336.138', 'aut_centralizer_order': 6, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 6, 'centralizer': '56.a1.a1', 'complements': ['168.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '6.a1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5300, 8593, 5281, 9258, 5091, 9204, 2347, 919], 'generators': [1, 112, 168, 84, 48], 'label': '336.138.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 65538728
    {'ambient': '336.138', 'aut_centralizer_order': 144, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '14.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.d1.a1', '42.a1.a1', '42.c1.a1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5300, -1, 5227, -1, 6216, -1, 5835, -1], 'generators': [1, 168], 'label': '336.138.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538729
    {'ambient': '336.138', 'aut_centralizer_order': 144, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '14.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '28.d1.b1', '42.a1.b1', '42.c1.b1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.c1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5300, -1, 4416, -1, 6216, -1, 6432, -1], 'generators': [181, 168], 'label': '336.138.84.c1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.c1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538730
    {'ambient': '336.138', 'aut_centralizer_order': 672, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.c1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1'], 'contains': ['168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2491, -1, 6901, -1, 7087, -1, 7466, -1], 'generators': [2], 'label': '336.138.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538731
    {'ambient': '336.138', 'aut_centralizer_order': 48, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '42.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.e1.a1', '42.a1.b1', '42.c1.a1', '42.e1.a1'], 'contains': ['168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1309, -1, 5965, -1, 6616, -1, 8449, -1], 'generators': [3], 'label': '336.138.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538732
    {'ambient': '336.138', 'aut_centralizer_order': 48, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '42.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '28.e1.b1', '42.a1.a1', '42.c1.b1', '42.e1.a1'], 'contains': ['168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1309, -1, 8937, -1, 6616, -1, 6985, -1], 'generators': [295], 'label': '336.138.84.e1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.e1.b1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538733
    {'ambient': '336.138', 'aut_centralizer_order': 2016, 'aut_label': '112.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2016, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.c1.b1'], 'contains': ['336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8352, 4343, 703, 4388, 2442, 5161, 3515, 5853], 'generators': [112], 'label': '336.138.112.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '336.138', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.5', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 65538734
    {'ambient': '336.138', 'aut_centralizer_order': 4032, 'aut_label': '168.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4032, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.b1.a1', '84.c1.a1', '84.c1.b1', '84.d1.a1', '84.e1.a1', '84.e1.b1'], 'contains': ['336.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5454, 6354, 5598, 5862, 5998, 5989, 6570, 5220], 'generators': [168], 'label': '336.138.168.a1.a1', 'mobius_quo': -1, 'mobius_sub': -168, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.50', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538735
    {'ambient': '336.138', 'aut_centralizer_order': 672, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4032, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.b1.a1', '84.b1.a1'], 'contains': ['336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8697, -1, 568, -1, 2806, -1, 3253, -1], 'generators': [198], 'label': '336.138.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '168.b1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538736
    {'ambient': '336.138', 'aut_centralizer_order': 144, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4032, 'centralizer': '14.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.c1.a1', '84.c1.a1'], 'contains': ['336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7960, -1, 1650, -1, 3536, -1, 2991, -1], 'generators': [1], 'label': '336.138.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '168.c1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538737
    {'ambient': '336.138', 'aut_centralizer_order': 144, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4032, 'centralizer': '14.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.c1.b1', '84.c1.b1'], 'contains': ['336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7960, -1, 1145, -1, 3536, -1, 3778, -1], 'generators': [181], 'label': '336.138.168.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.b1', 'old_label': '168.c1.b1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538738
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 2, 'centralizer': '168.a1.a1', 'complements': ['168.b1.a1', '168.c1.a1', '168.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.e1.b1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [906, 6690, 9489, 7844, 6276, 4540, 5787, 4683], 'generators': [3, 168, 112, 84, 48], 'label': '336.138.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 65538739
    {'ambient': '336.138', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.c1.a1', '168.c1.b1'], 'contains': [], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8352, 6354, 980, 5314, 3171, 5989, 3384, 5220], 'generators': [], 'label': '336.138.336.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 65538740
    {'ambient': '336.138', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 6, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3048, -1, 8122, -1, 8247, -1, 3978, -1], 'generators': [1, 84, 168, 2, 48], 'label': '336.138.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}