Abstract group data - 1728.46354

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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': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 12, 6, 6, 6, 6], 'aut_gens': [[46999, 823312, 835777, 357943, 1174837], [1644641, 264280, 1394809, 1485655, 358375], [58339, 623516, 1172621, 335263, 1462543], [1342360, 963709, 52001, 1174405, 1462543], [409220, 939733, 275485, 1174405, 1462543], [46999, 1663750, 275485, 357943, 1174837], [793511, 87164, 612293, 1462975, 1174837], [409220, 623516, 1172621, 1174405, 334399]], 'aut_group': None, 'aut_hash': 5675430861318798311, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 24, 'aut_perms': [433752710349044461204282, 382762025270755244553144, 392074860512021177671708, 589188335951011591656922, 6819201568181153646008, 158829126683670736894707, 582440387933007198410635], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 6, 2, 1], [2, 18, 1, 2], [2, 36, 1, 1], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 1, 1], [3, 16, 1, 2], [3, 32, 1, 1], [4, 6, 1, 1], [4, 6, 2, 1], [4, 18, 1, 1], [4, 36, 1, 3], [4, 108, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 4], [6, 6, 2, 1], [6, 8, 1, 1], [6, 12, 1, 2], [6, 12, 2, 2], [6, 16, 1, 2], [6, 18, 2, 1], [6, 24, 2, 1], [6, 32, 1, 1], [6, 36, 2, 1], [6, 48, 1, 1], [6, 48, 2, 1], [6, 144, 1, 1], [12, 6, 2, 1], [12, 12, 2, 2], [12, 18, 2, 1], [12, 24, 2, 1], [12, 36, 2, 3], [12, 48, 1, 1], [12, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4.D_6^2.C_2^2', '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': 12, 'autcentquo_group': '864.4673', 'autcentquo_hash': 4673, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 3], [2, 18, 2], [2, 36, 1], [2, 54, 1], [2, 108, 1], [3, 2, 2], [3, 4, 1], [3, 8, 1], [3, 16, 2], [3, 32, 1], [4, 6, 3], [4, 18, 1], [4, 36, 3], [4, 108, 1], [6, 2, 2], [6, 4, 1], [6, 6, 6], [6, 8, 1], [6, 12, 6], [6, 16, 2], [6, 18, 2], [6, 24, 2], [6, 32, 1], [6, 36, 2], [6, 48, 3], [6, 144, 1], [12, 6, 2], [12, 12, 4], [12, 18, 2], [12, 24, 2], [12, 36, 6], [12, 48, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '864.4673', 'commutator_count': 1, 'commutator_label': '216.173', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46354, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['72.23', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 3], [2, 18, 1, 2], [2, 36, 1, 1], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 1, 1], [3, 16, 1, 2], [3, 32, 1, 1], [4, 6, 1, 3], [4, 18, 1, 1], [4, 36, 1, 3], [4, 108, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 4], [6, 6, 2, 1], [6, 8, 1, 1], [6, 12, 1, 6], [6, 16, 1, 2], [6, 18, 2, 1], [6, 24, 1, 2], [6, 32, 1, 1], [6, 36, 2, 1], [6, 48, 1, 1], [6, 48, 2, 1], [6, 144, 1, 1], [12, 6, 2, 1], [12, 12, 1, 4], [12, 18, 2, 1], [12, 24, 1, 2], [12, 36, 2, 3], [12, 48, 1, 1], [12, 48, 2, 1]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 161280, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4673', 'hash': 46354, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 2, 6, 6], 'inner_gens': [[46999, 380701, 835777, 357943, 334399], [1342360, 823312, 52001, 646513, 334399], [46999, 87164, 835777, 357943, 646081], [46999, 543166, 835777, 357943, 1174837], [886789, 800632, 275485, 357943, 1174837]], 'inner_hash': 4673, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': 'S_4\\times S_3^2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 22], [3, 8], [4, 13], [6, 18], [8, 2], [12, 4]], 'label': '1728.46354', 'linC_count': 400, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 16, 'linQ_dim': 7, 'linQ_dim_count': 16, 'linR_count': 144, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^3.S3^3', 'ngens': 9, '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, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 57, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 75, 'number_divisions': 65, 'number_normal_subgroups': 68, 'number_subgroup_autclasses': 985, 'number_subgroup_classes': 1151, 'number_subgroups': 16440, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 259], [3, 80], [4, 252], [6, 632], [12, 504]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [46657, 46657, 46657], 'outer_gens': [[793511, 380701, 835777, 357943, 1485223], [46999, 823312, 835777, 357943, 646081], [46999, 823312, 835777, 1462975, 1174837]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [3, 8], [4, 13], [6, 10], [8, 4], [12, 8]], 'representations': {'PC': {'code': 19085719519911697027292076466694454136394235075525877596378181, 'gens': [1, 2, 4, 6, 8], 'pres': [9, 2, 2, 3, 2, 2, 2, 3, 2, 3, 181, 46, 218, 660, 102, 25934, 12335, 158, 6063, 31111, 15568, 23353, 8674, 214, 7811]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 793169, 478576, 909811, 47465, 502525, 1394809, 1197949, 70633]}, 'Perm': {'d': 14, 'gens': [6266977920, 12493958520, 19678982405, 19678982400, 3, 403200, 840, 7, 16]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.S_3^3', 'transitive_degree': 36, '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: 172486258
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 46354, 'group_order': 1728, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 46657, 'size': 1}
  • id: 172486269
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 46354, 'group_order': 1728, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 793169, 'size': 1}
  • id: 172486280
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 3, 'group_counter': 46354, 'group_order': 1728, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 817145, 'size': 3}
  • id: 172486291
    {'aut_label': '2C', 'centralizer': '3.b1.a1', 'counter': 4, 'group_counter': 46354, 'group_order': 1728, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 887131, 'size': 3}
  • id: 172486302
    {'aut_label': '2D', 'centralizer': '6.l1.a1', 'counter': 5, 'group_counter': 46354, 'group_order': 1728, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1674451, 'size': 6}
  • id: 172486313
    {'aut_label': '2E', 'centralizer': '6.d1.a1', 'counter': 6, 'group_counter': 46354, 'group_order': 1728, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 46999, 'size': 6}
  • id: 172486324
    {'aut_label': '2E', 'centralizer': '6.d1.a1', 'counter': 7, 'group_counter': 46354, 'group_order': 1728, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 793511, 'size': 6}
  • id: 172486331
    {'aut_label': '2G', 'centralizer': '18.q1.a1', 'counter': 8, 'group_counter': 46354, 'group_order': 1728, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 1651771, 'size': 18}
  • id: 172486332
    {'aut_label': '2H', 'centralizer': '18.bf1.a1', 'counter': 9, 'group_counter': 46354, 'group_order': 1728, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 887075, 'size': 18}
  • id: 172486259
    {'aut_label': '2I', 'centralizer': '36.d1.a1', 'counter': 10, 'group_counter': 46354, 'group_order': 1728, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 822979, 'size': 36}
  • id: 172486260
    {'aut_label': '2J', 'centralizer': '54.l1.a1', 'counter': 11, 'group_counter': 46354, 'group_order': 1728, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 264469, 'size': 54}
  • id: 172486261
    {'aut_label': '2K', 'centralizer': '108.h1.a1', 'counter': 12, 'group_counter': 46354, 'group_order': 1728, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 1186859, 'size': 108}
  • id: 172486262
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 46354, 'group_order': 1728, 'label': '3A', 'order': 3, 'powers': [13, 1], 'representative': 1197517, 'size': 2}
  • id: 172486263
    {'aut_label': '3B', 'centralizer': '2.e1.a1', 'counter': 14, 'group_counter': 46354, 'group_order': 1728, 'label': '3B', 'order': 3, 'powers': [14, 1], 'representative': 1198381, 'size': 2}
  • id: 172486264
    {'aut_label': '3C', 'centralizer': '4.b1.a1', 'counter': 15, 'group_counter': 46354, 'group_order': 1728, 'label': '3C', 'order': 3, 'powers': [15, 1], 'representative': 622969, 'size': 4}
  • id: 172486265
    {'aut_label': '3D', 'centralizer': '8.d1.a1', 'counter': 16, 'group_counter': 46354, 'group_order': 1728, 'label': '3D', 'order': 3, 'powers': [16, 1], 'representative': 899128, 'size': 8}
  • id: 172486266
    {'aut_label': '3E', 'centralizer': '16.b1.a1', 'counter': 17, 'group_counter': 46354, 'group_order': 1728, 'label': '3E', 'order': 3, 'powers': [17, 1], 'representative': 370336, 'size': 16}
  • id: 172486267
    {'aut_label': '3F', 'centralizer': '16.g1.a1', 'counter': 18, 'group_counter': 46354, 'group_order': 1728, 'label': '3F', 'order': 3, 'powers': [18, 1], 'representative': 767155, 'size': 16}
  • id: 172486268
    {'aut_label': '3G', 'centralizer': '32.a1.a1', 'counter': 19, 'group_counter': 46354, 'group_order': 1728, 'label': '3G', 'order': 3, 'powers': [19, 1], 'representative': 1474108, 'size': 32}
  • id: 172486270
    {'aut_label': '4A', 'centralizer': '6.y1.a1', 'counter': 20, 'group_counter': 46354, 'group_order': 1728, 'label': '4A', 'order': 4, 'powers': [2, 20], 'representative': 52001, 'size': 6}
  • id: 172486271
    {'aut_label': '4B', 'centralizer': '6.f1.a1', 'counter': 21, 'group_counter': 46354, 'group_order': 1728, 'label': '4B', 'order': 4, 'powers': [4, 21], 'representative': 910783, 'size': 6}
  • id: 172486272
    {'aut_label': '4B', 'centralizer': '6.f1.a1', 'counter': 22, 'group_counter': 46354, 'group_order': 1728, 'label': '4C', 'order': 4, 'powers': [4, 22], 'representative': 1657295, 'size': 6}
  • id: 172486273
    {'aut_label': '4D', 'centralizer': '18.be1.a1', 'counter': 23, 'group_counter': 46354, 'group_order': 1728, 'label': '4D', 'order': 4, 'powers': [2, 23], 'representative': 892475, 'size': 18}
  • id: 172486274
    {'aut_label': '4E', 'centralizer': '36.z1.a1', 'counter': 24, 'group_counter': 46354, 'group_order': 1728, 'label': '4E', 'order': 4, 'powers': [2, 24], 'representative': 52343, 'size': 36}
  • id: 172486275
    {'aut_label': '4F', 'centralizer': '36.h1.a1', 'counter': 25, 'group_counter': 46354, 'group_order': 1728, 'label': '4F', 'order': 4, 'powers': [4, 25], 'representative': 800281, 'size': 36}
  • id: 172486276
    {'aut_label': '4G', 'centralizer': '36.ci1.a1', 'counter': 26, 'group_counter': 46354, 'group_order': 1728, 'label': '4G', 'order': 4, 'powers': [3, 26], 'representative': 355799, 'size': 36}
  • id: 172486277
    {'aut_label': '4H', 'centralizer': '108.r1.a1', 'counter': 27, 'group_counter': 46354, 'group_order': 1728, 'label': '4H', 'order': 4, 'powers': [4, 27], 'representative': 370163, 'size': 108}
  • id: 172486278
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 46354, 'group_order': 1728, 'label': '6A', 'order': 6, 'powers': [13, 2], 'representative': 264413, 'size': 2}
  • id: 172486279
    {'aut_label': '6B', 'centralizer': '2.e1.a1', 'counter': 29, 'group_counter': 46354, 'group_order': 1728, 'label': '6B', 'order': 6, 'powers': [14, 2], 'representative': 1369013, 'size': 2}
  • id: 172486281
    {'aut_label': '6C', 'centralizer': '4.b1.a1', 'counter': 30, 'group_counter': 46354, 'group_order': 1728, 'label': '6C', 'order': 6, 'powers': [15, 2], 'representative': 1369445, 'size': 4}
  • id: 172486282
    {'aut_label': '6D', 'centralizer': '6.o1.a1', 'counter': 31, 'group_counter': 46354, 'group_order': 1728, 'label': '6D', 'order': 6, 'powers': [13, 3], 'representative': 1392557, 'size': 6}
  • id: 172486283
    {'aut_label': '6E', 'centralizer': '6.o1.a1', 'counter': 32, 'group_counter': 46354, 'group_order': 1728, 'label': '6E', 'order': 6, 'powers': [13, 4], 'representative': 1462543, 'size': 6}
  • id: 172486284
    {'aut_label': '6F', 'centralizer': '6.u1.a1', 'counter': 33, 'group_counter': 46354, 'group_order': 1728, 'label': '6F', 'order': 6, 'powers': [14, 4], 'representative': 646513, 'size': 6}
  • id: 172486285
    {'aut_label': '6G', 'centralizer': '6.u1.a1', 'counter': 34, 'group_counter': 46354, 'group_order': 1728, 'label': '6G', 'order': 6, 'powers': [14, 3], 'representative': 529871, 'size': 6}
  • id: 172486286
    {'aut_label': '6H1', 'centralizer': '6.l1.a1', 'counter': 35, 'group_counter': 46354, 'group_order': 1728, 'label': '6H1', 'order': 6, 'powers': [13, 5], 'representative': 1114567, 'size': 6}
  • id: 172486287
    {'aut_label': '6H1', 'centralizer': '6.l1.a1', 'counter': 36, 'group_counter': 46354, 'group_order': 1728, 'label': '6H-1', 'order': 6, 'powers': [13, 5], 'representative': 554719, 'size': 6}
  • id: 172486288
    {'aut_label': '6I', 'centralizer': '8.d1.a1', 'counter': 37, 'group_counter': 46354, 'group_order': 1728, 'label': '6I', 'order': 6, 'powers': [16, 2], 'representative': 1645604, 'size': 8}
  • id: 172486289
    {'aut_label': '6J', 'centralizer': '12.j1.a1', 'counter': 38, 'group_counter': 46354, 'group_order': 1728, 'label': '6J', 'order': 6, 'powers': [13, 6], 'representative': 622411, 'size': 12}
  • id: 172486290
    {'aut_label': '6K', 'centralizer': '12.s1.a1', 'counter': 39, 'group_counter': 46354, 'group_order': 1728, 'label': '6K', 'order': 6, 'powers': [14, 6], 'representative': 622843, 'size': 12}
  • id: 172486292
    {'aut_label': '6L', 'centralizer': '12.bn1.a1', 'counter': 40, 'group_counter': 46354, 'group_order': 1728, 'label': '6L', 'order': 6, 'powers': [15, 3], 'representative': 816713, 'size': 12}
  • id: 172486293
    {'aut_label': '6J', 'centralizer': '12.j1.a1', 'counter': 41, 'group_counter': 46354, 'group_order': 1728, 'label': '6M', 'order': 6, 'powers': [13, 7], 'representative': 264719, 'size': 12}
  • id: 172486294
    {'aut_label': '6K', 'centralizer': '12.s1.a1', 'counter': 42, 'group_counter': 46354, 'group_order': 1728, 'label': '6N', 'order': 6, 'powers': [14, 7], 'representative': 265583, 'size': 12}
  • id: 172486295
    {'aut_label': '6O', 'centralizer': '12.bn1.a1', 'counter': 43, 'group_counter': 46354, 'group_order': 1728, 'label': '6O', 'order': 6, 'powers': [15, 4], 'representative': 886699, 'size': 12}
  • id: 172486296
    {'aut_label': '6P', 'centralizer': '16.b1.a1', 'counter': 44, 'group_counter': 46354, 'group_order': 1728, 'label': '6P', 'order': 6, 'powers': [17, 2], 'representative': 1512767, 'size': 16}
  • id: 172486297
    {'aut_label': '6Q', 'centralizer': '16.g1.a1', 'counter': 45, 'group_counter': 46354, 'group_order': 1728, 'label': '6Q', 'order': 6, 'powers': [18, 2], 'representative': 1116416, 'size': 16}
  • id: 172486298
    {'aut_label': '6R1', 'centralizer': '18.q1.a1', 'counter': 46, 'group_counter': 46354, 'group_order': 1728, 'label': '6R1', 'order': 6, 'powers': [13, 8], 'representative': 532039, 'size': 18}
  • id: 172486299
    {'aut_label': '6R1', 'centralizer': '18.q1.a1', 'counter': 47, 'group_counter': 46354, 'group_order': 1728, 'label': '6R-1', 'order': 6, 'powers': [13, 8], 'representative': 1394713, 'size': 18}
  • id: 172486300
    {'aut_label': '6S', 'centralizer': '24.h1.a1', 'counter': 48, 'group_counter': 46354, 'group_order': 1728, 'label': '6S', 'order': 6, 'powers': [15, 6], 'representative': 1198291, 'size': 24}
  • id: 172486301
    {'aut_label': '6S', 'centralizer': '24.h1.a1', 'counter': 49, 'group_counter': 46354, 'group_order': 1728, 'label': '6T', 'order': 6, 'powers': [15, 7], 'representative': 1369787, 'size': 24}
  • id: 172486303
    {'aut_label': '6U', 'centralizer': '32.a1.a1', 'counter': 50, 'group_counter': 46354, 'group_order': 1728, 'label': '6U', 'order': 6, 'powers': [19, 2], 'representative': 938219, 'size': 32}
  • id: 172486304
    {'aut_label': '6V1', 'centralizer': '36.d1.a1', 'counter': 51, 'group_counter': 46354, 'group_order': 1728, 'label': '6V1', 'order': 6, 'powers': [13, 10], 'representative': 263095, 'size': 36}
  • id: 172486305
    {'aut_label': '6V1', 'centralizer': '36.d1.a1', 'counter': 52, 'group_counter': 46354, 'group_order': 1728, 'label': '6V-1', 'order': 6, 'powers': [13, 10], 'representative': 1382863, 'size': 36}
  • id: 172486306
    {'aut_label': '6W', 'centralizer': '48.h1.a1', 'counter': 53, 'group_counter': 46354, 'group_order': 1728, 'label': '6W', 'order': 6, 'powers': [16, 5], 'representative': 380701, 'size': 48}
  • id: 172486307
    {'aut_label': '6X1', 'centralizer': '48.h1.a1', 'counter': 54, 'group_counter': 46354, 'group_order': 1728, 'label': '6X1', 'order': 6, 'powers': [17, 5], 'representative': 1220323, 'size': 48}
  • id: 172486308
    {'aut_label': '6X1', 'centralizer': '48.h1.a1', 'counter': 55, 'group_counter': 46354, 'group_order': 1728, 'label': '6X-1', 'order': 6, 'powers': [17, 5], 'representative': 1103014, 'size': 48}
  • id: 172486309
    {'aut_label': '6Y', 'centralizer': '144.r1.a1', 'counter': 56, 'group_counter': 46354, 'group_order': 1728, 'label': '6Y', 'order': 6, 'powers': [16, 9], 'representative': 479159, 'size': 144}
  • id: 172486310
    {'aut_label': '12A1', 'centralizer': '6.y1.a1', 'counter': 57, 'group_counter': 46354, 'group_order': 1728, 'label': '12A1', 'order': 12, 'powers': [29, 20], 'representative': 1395661, 'size': 6}
  • id: 172486311
    {'aut_label': '12A1', 'centralizer': '6.y1.a1', 'counter': 58, 'group_counter': 46354, 'group_order': 1728, 'label': '12A5', 'order': 12, 'powers': [29, 20], 'representative': 275929, 'size': 6}
  • id: 172486312
    {'aut_label': '12B', 'centralizer': '12.n1.a1', 'counter': 59, 'group_counter': 46354, 'group_order': 1728, 'label': '12B', 'order': 12, 'powers': [32, 21], 'representative': 1175161, 'size': 12}
  • id: 172486314
    {'aut_label': '12B', 'centralizer': '12.n1.a1', 'counter': 60, 'group_counter': 46354, 'group_order': 1728, 'label': '12C', 'order': 12, 'powers': [32, 22], 'representative': 1392881, 'size': 12}
  • id: 172486315
    {'aut_label': '12D', 'centralizer': '12.bi1.a1', 'counter': 61, 'group_counter': 46354, 'group_order': 1728, 'label': '12D', 'order': 12, 'powers': [33, 21], 'representative': 1630264, 'size': 12}
  • id: 172486316
    {'aut_label': '12D', 'centralizer': '12.bi1.a1', 'counter': 62, 'group_counter': 46354, 'group_order': 1728, 'label': '12E', 'order': 12, 'powers': [33, 22], 'representative': 121316, 'size': 12}
  • id: 172486317
    {'aut_label': '12F1', 'centralizer': '18.be1.a1', 'counter': 63, 'group_counter': 46354, 'group_order': 1728, 'label': '12F1', 'order': 12, 'powers': [29, 23], 'representative': 1115071, 'size': 18}
  • id: 172486318
    {'aut_label': '12F1', 'centralizer': '18.be1.a1', 'counter': 64, 'group_counter': 46354, 'group_order': 1728, 'label': '12F5', 'order': 12, 'powers': [29, 23], 'representative': 252361, 'size': 18}
  • id: 172486319
    {'aut_label': '12G', 'centralizer': '24.o1.a1', 'counter': 65, 'group_counter': 46354, 'group_order': 1728, 'label': '12G', 'order': 12, 'powers': [43, 21], 'representative': 70093, 'size': 24}
  • id: 172486320
    {'aut_label': '12G', 'centralizer': '24.o1.a1', 'counter': 66, 'group_counter': 46354, 'group_order': 1728, 'label': '12H', 'order': 12, 'powers': [43, 22], 'representative': 817037, 'size': 24}
  • id: 172486321
    {'aut_label': '12I1', 'centralizer': '36.z1.a1', 'counter': 67, 'group_counter': 46354, 'group_order': 1728, 'label': '12I1', 'order': 12, 'powers': [29, 24], 'representative': 1394707, 'size': 36}
  • id: 172486322
    {'aut_label': '12I1', 'centralizer': '36.z1.a1', 'counter': 68, 'group_counter': 46354, 'group_order': 1728, 'label': '12I5', 'order': 12, 'powers': [29, 24], 'representative': 1114765, 'size': 36}
  • id: 172486323
    {'aut_label': '12J1', 'centralizer': '36.h1.a1', 'counter': 69, 'group_counter': 46354, 'group_order': 1728, 'label': '12J1', 'order': 12, 'powers': [32, 25], 'representative': 520375, 'size': 36}
  • id: 172486325
    {'aut_label': '12J1', 'centralizer': '36.h1.a1', 'counter': 70, 'group_counter': 46354, 'group_order': 1728, 'label': '12J-1', 'order': 12, 'powers': [32, 25], 'representative': 1359721, 'size': 36}
  • id: 172486326
    {'aut_label': '12K1', 'centralizer': '36.ci1.a1', 'counter': 71, 'group_counter': 46354, 'group_order': 1728, 'label': '12K1', 'order': 12, 'powers': [34, 26], 'representative': 252685, 'size': 36}
  • id: 172486327
    {'aut_label': '12K1', 'centralizer': '36.ci1.a1', 'counter': 72, 'group_counter': 46354, 'group_order': 1728, 'label': '12K5', 'order': 12, 'powers': [34, 26], 'representative': 1652395, 'size': 36}
  • id: 172486328
    {'aut_label': '12L', 'centralizer': '48.bj1.a1', 'counter': 73, 'group_counter': 46354, 'group_order': 1728, 'label': '12L', 'order': 12, 'powers': [37, 20], 'representative': 1523875, 'size': 48}
  • id: 172486329
    {'aut_label': '12M1', 'centralizer': '48.bj1.a1', 'counter': 74, 'group_counter': 46354, 'group_order': 1728, 'label': '12M1', 'order': 12, 'powers': [45, 20], 'representative': 1522987, 'size': 48}
  • id: 172486330
    {'aut_label': '12M1', 'centralizer': '48.bj1.a1', 'counter': 75, 'group_counter': 46354, 'group_order': 1728, 'label': '12M5', 'order': 12, 'powers': [45, 20], 'representative': 520528, 'size': 48}
• 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: 17499065
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1a', '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, 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: 17499076
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1b', '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, 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: 17499087
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1c', '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, 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: 17499098
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1d', '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, -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: 17499109
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1e', '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, -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: 17499120
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1f', '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, -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: 17499127
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1g', '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, -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: 17499128
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.1h', '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, 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: 17499129
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 2, 0, 2, 0, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 17499066
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, -1, -1, -1, -1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 2, 0, 0, 2, -1, -1, 2, 2, 0, 0, -1, 0, 0, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 17499067
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 2, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499068
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 0, 0, -2, -2, -2, -2, 2, 2, 2, -2, -2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499069
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 0, 0, -2, 2, 2, -2, -2, -2, 2, -2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499070
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, -2, -2, 0, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 1, 1, 2, 1, -2, -1, 1, -2, -1, -1, 2, 1, 1, 1, 1, -1, -1, -1, -2, 1, 1, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499071
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, -2, -2, 0, -2, 0, 2, 2, 2, -1, -1, -1, -1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2, -1, 0, 0, 2, 0, 0, 2, -1, -1, -2, -2, 0, 0, -1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 17499072
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, -2, 2, 0, 2, 0, 2, 2, 2, -1, -1, -1, -1, -2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2, -1, 0, 0, 2, 0, 0, 2, -1, -1, -2, -2, 0, 0, -1, 0, 0, 1, 1, 1, -1, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
  • id: 17499073
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 2, -2, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 2, 2, 0, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 1, 1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 1, 1, -1, -1, -1, 1, 1, -2, 1, 1, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499074
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, -2, -2, 2, 0, 2, 0, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, -2, 1, -1, -2, 1, -1, 2, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 0, -1, -1, 0, -1, -1, -2, 1, 1], 'schur_index': 1}
  • id: 17499075
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, -1, -1, 2, -2, -2, 2, -2, 0, -2, 0, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, -2, 1, -1, -2, 1, -1, 2, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -2, -2, -1, -1, 1, 1, 0, 1, 1, 0, 1, 1, 2, -1, -1], 'schur_index': 1}
  • id: 17499077
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, -1, -1, -2, 2, 2, -2, -2, 0, -2, 0, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 2, 2, 1, 1, -1, -1, 0, 1, 1, 0, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 17499078
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2m', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, 2, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, -2, -2, 0, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, 1, -2, -1, 1, -2, -1, -1, 2, -1, -1, 1, 1, -1, 1, 1, 2, -1, -1, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499079
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2n', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, 2, -2, 0, -2, 0, 2, 2, 2, -1, -1, -1, -1, -2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 2, 0, 0, 2, -1, -1, 2, 2, 0, 0, -1, 0, 0, -1, -1, -1, 1, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
  • id: 17499084
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 1, 1, -1, 3, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 3, -1, -1, -1, 1, -1, -1, -1, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, 1, 1, -1, 1, 1, -1, 0, 0, -1, -1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499085
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 3, 1, 1, -1, -1, 1, 1, 1, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 3, 3, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499086
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, -1, 1, -3, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 3, 1, 1, -1, -1, -1, 1, -1, 3, 3, 3, -1, -1, -1, -1, -3, -3, 0, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 3, 3, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499088
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, -1, 1, 3, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, -3, 1, 1, 1, 1, -1, -1, 1, 3, 3, 3, -1, -1, -1, -1, -3, -3, 0, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 1, 1, 0, 0, 0, 0, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499089
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, 1, 1, 1, -3, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 3, -1, -1, -1, 1, 1, -1, 1, 3, 3, 3, -1, -1, -1, -1, -3, -3, 0, 1, 1, -1, 1, 1, -1, 0, 0, 1, 1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499090
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, 1, 1, 1, 3, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -3, -1, -1, 1, -1, 1, 1, -1, 3, 3, 3, -1, -1, -1, -1, -3, -3, 0, 1, 1, -1, 1, 1, -1, 0, 0, 1, 1, 1, 1, 0, -1, -1, 0, 0, 0, 0, -3, -3, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499091
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, -1, -1, -3, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, -3, 1, 1, 1, 1, 1, -1, -1, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499092
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 1, 1, -1, -3, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -3, -1, -1, 1, -1, -1, 1, 1, 3, 3, 3, -1, -1, -1, -1, 3, 3, 0, 1, 1, -1, 1, 1, -1, 0, 0, -1, -1, 1, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499080
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2o', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, 4, -2, -2, 4, 4, -2, -2, 0, -4, 4, 0, 0, 0, 0, 0, -4, 2, 2, 2, -4, -2, 4, 0, 0, -4, -4, 2, 2, 4, -2, -2, -4, 2, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -4, 4, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499081
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2p', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, 4, -2, -2, 4, 4, -2, -2, 0, 4, -4, 0, 0, 0, 0, 0, -4, 2, 2, 2, -4, -2, 4, 0, 0, -4, 4, -2, 2, -4, 2, -2, -4, 2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, -4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499082
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2q', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, 0, -4, 4, 0, 0, 0, 0, 0, 2, -4, 2, -4, 2, 4, -2, 0, 0, -4, 2, -4, 2, -2, 4, -2, 2, -4, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499083
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.2r', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, 0, 4, -4, 0, 0, 0, 0, 0, 2, -4, 2, -4, 2, 4, -2, 0, 0, -4, -2, 4, 2, 2, -4, -2, 2, -4, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499093
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4, 0, 0, 4, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, 4, 0, 0, -2, 0, 0, -2, 0, 0, -2, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1], 'schur_index': 1}
  • id: 17499094
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, 0, 0, 4, -2, -2, 1, -2, -2, 1, -2, -2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499095
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, 0, 0, -2, 0, 0, -2, 1, -2, -2, -2, 0, 0, 1, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499096
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4d', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, 0, 0, 2, 0, 0, -4, 0, 0, 4, 2, 2, 0, 0, 0, 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], 'schur_index': 1}
  • id: 17499097
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, 0, 0, -4, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, 2, 2, -2, 0, 0, -2, 0, 0, -2, 1, -2, 2, 2, 0, 0, 1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499099
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, -4, -4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, -4, -4, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, 0, 0, 4, 2, 2, 1, 2, 2, 1, -2, -2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499100
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4g', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, -4, 0, 0, -4, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, 4, 0, 0, -2, 0, 0, -2, 0, 0, -2, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1], 'schur_index': 1}
  • id: 17499101
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4h', 'multiplicity': 1, 'nt': [12, 38], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 2, 2, -1, 2, 2, -2, -2, 0, 0, -4, 2, 2, -1, -2, -2, 1, 2, 2, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499102
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4i', 'multiplicity': 1, 'nt': [12, 38], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 4, -4, 0, 0, 0, 0, 0, 2, 2, -1, 2, 2, -2, -2, 0, 0, -4, -2, -2, -1, 2, 2, 1, 2, 2, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499105
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6a', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 6, -2, -2, -2, 2, 0, -2, 0, 6, -3, -3, 1, -2, 1, -2, 0, 0, 0, 2, -1, 1, 2, -1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -3, -3, 1, 1, -2, -2, 1, 1, 1, 1, 0, -1, 1, 0, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499106
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6b', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, 2, 2, -2, 0, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -3, 6, -3, -2, 1, -2, 1, -3, -3, 0, -1, 2, 1, -1, 2, 1, 0, 0, 1, 1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499107
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6c', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -6, -6, -6, 2, 2, -2, -2, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499108
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6d', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -6, -6, -6, 2, 2, -2, -2, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499110
    {'cdim': 6, 'counter': 50, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6e', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 6, 2, 2, -2, -2, 0, 2, 0, 6, -3, -3, 1, -2, 1, -2, 0, 0, 0, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -3, -3, -1, -1, 2, 2, 1, 1, -1, -1, 0, 1, -1, 0, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499111
    {'cdim': 6, 'counter': 51, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6f', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, -2, -2, -2, 0, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, -3, 6, -3, -2, 1, -2, 1, -3, -3, 0, 1, -2, 1, 1, -2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499112
    {'cdim': 6, 'counter': 52, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6g', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -6, -2, -2, 2, 0, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -3, 6, -3, -2, 1, -2, 1, 3, 3, 0, 1, -2, 1, 1, -2, 1, 0, 0, -1, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499113
    {'cdim': 6, 'counter': 53, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6h', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -6, 2, 2, 2, 0, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, -3, 6, -3, -2, 1, -2, 1, 3, 3, 0, -1, 2, 1, -1, 2, 1, 0, 0, -1, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499114
    {'cdim': 6, 'counter': 54, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6i', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, -6, 2, 2, 2, 2, 0, -2, 0, 6, -3, -3, 1, -2, 1, -2, 0, 0, 0, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 3, 3, -1, -1, 2, 2, -1, -1, -1, -1, 0, -1, 1, 0, 1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 17499115
    {'cdim': 6, 'counter': 55, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6j', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, -6, -2, -2, 2, -2, 0, 2, 0, 6, -3, -3, 1, -2, 1, -2, 0, 0, 0, 2, -1, 1, 2, -1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 3, 3, 1, 1, -2, -2, -1, -1, 1, 1, 0, 1, -1, 0, -1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 17499103
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4j', 'multiplicity': 2, 'nt': [24, 204], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 4, -8, 4, 8, -4, 0, 0, 4, 0, 0, 4, 0, 0, -4, -2, 4, 0, 0, 0, 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], 'schur_index': 1}
  • id: 17499104
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.4k', 'multiplicity': 2, 'nt': [24, 229], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, 4, -8, -4, 8, 0, 0, 4, 0, 0, 4, 0, 0, -4, 4, -2, 0, 0, 0, 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], 'schur_index': 1}
  • id: 17499121
    {'cdim': 8, 'counter': 60, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, -4, -4, -4, 0, 0, -4, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499122
    {'cdim': 8, 'counter': 61, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.8b', 'multiplicity': 1, 'nt': [24, 1295], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, 4, 4, -4, -4, 0, 0, 4, 0, 0, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499116
    {'cdim': 6, 'counter': 56, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6k', 'multiplicity': 2, 'nt': [36, 771], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 6, -12, 6, 4, -2, -4, 2, 0, 0, 0, 2, -4, -2, -2, 4, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499117
    {'cdim': 6, 'counter': 57, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6l', 'multiplicity': 2, 'nt': [36, 771], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 6, -12, 6, 4, -2, -4, 2, 0, 0, 0, -2, 4, -2, 2, -4, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499118
    {'cdim': 6, 'counter': 58, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6m', 'multiplicity': 2, 'nt': [36, 800], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -12, 6, 6, -2, 4, 2, -4, 0, 0, 0, -4, 2, -2, 4, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, -4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499119
    {'cdim': 6, 'counter': 59, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.6n', 'multiplicity': 2, 'nt': [36, 800], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, -12, 6, 6, -2, 4, 2, -4, 0, 0, 0, 4, -2, -2, -4, 2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -4, 4, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499123
    {'cdim': 12, 'counter': 62, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.12a', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 4, 4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, -6, -6, 3, 2, 2, 2, 2, 0, 0, 0, -2, -2, -1, -2, -2, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499124
    {'cdim': 12, 'counter': 63, 'faithful': False, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.12b', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, -4, -4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, -6, -6, 3, 2, 2, 2, 2, 0, 0, 0, 2, 2, -1, 2, 2, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499125
    {'cdim': 12, 'counter': 64, 'faithful': True, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.12c', 'multiplicity': 1, 'nt': [36, 2466], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 6, 6, -3, -2, -2, 2, 2, 0, 0, 0, 2, 2, 1, -2, -2, -1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17499126
    {'cdim': 12, 'counter': 65, 'faithful': True, 'group': '1728.46354', 'group_order': 1728, 'image': None, 'label': '1728.46354.12d', 'multiplicity': 1, 'nt': [36, 2466], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 6, 6, -3, -2, -2, 2, 2, 0, 0, 0, -2, -2, 1, 2, 2, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 38234721
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1728, 'label': '1728.46354.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 38234732
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 864, 'label': '1728.46354.1b', '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]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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: 38234743
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 864, 'label': '1728.46354.1c', '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]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 38234754
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  • id: 38234765
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  • id: 38234776
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  • id: 38234787
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  • id: 38234794
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  • id: 38234795
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  • id: 38234722
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  • id: 38234723
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 288, 'label': '1728.46354.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234724
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 432, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 216, 'label': '1728.46354.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234725
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  • id: 38234726
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 144, 'label': '1728.46354.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234727
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.g1.a1', 'kernel_order': 144, 'label': '1728.46354.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38234728
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  • id: 38234729
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 144, 'label': '1728.46354.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234730
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 288, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.i1.a1', 'kernel_order': 144, 'label': '1728.46354.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38234731
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 288, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.h1.a1', 'kernel_order': 144, 'label': '1728.46354.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38234733
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 288, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 144, 'label': '1728.46354.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38234734
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 144, 'label': '1728.46354.2m', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234735
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 144, 'label': '1728.46354.2n', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 38234736
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 144, 'counter': 23, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.b1', 'kernel_order': 72, 'label': '1728.46354.2o1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 38234737
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 144, 'counter': 24, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.b1', 'kernel_order': 72, 'label': '1728.46354.2o2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 38234738
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 144, 'counter': 25, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 72, 'label': '1728.46354.2p1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 38234739
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 144, 'counter': 26, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 72, 'label': '1728.46354.2p2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 38234740
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 144, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.b1', 'kernel_order': 72, 'label': '1728.46354.2q1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234741
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 144, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.b1', 'kernel_order': 72, 'label': '1728.46354.2q2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234742
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 144, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 72, 'label': '1728.46354.2r1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234744
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 144, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 72, 'label': '1728.46354.2r2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234745
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.d1.a1', 'kernel_order': 72, 'label': '1728.46354.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234746
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.d1.a1', 'kernel_order': 72, 'label': '1728.46354.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234747
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 36, 'label': '1728.46354.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234748
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 36, 'label': '1728.46354.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234749
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 36, 'label': '1728.46354.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234750
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 36, 'label': '1728.46354.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234751
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  • id: 38234752
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 36, 'label': '1728.46354.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234753
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  • id: 38234755
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  • id: 38234756
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 48, 'label': '1728.46354.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234757
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  • id: 38234758
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 48, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.46354.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234759
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  • id: 38234760
    {'center': '36.c1.a1', 'center_index': 36, 'center_order': 48, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 24, 'label': '1728.46354.4g', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 38234761
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '72.23', 'image_order': 72, 'indicator': 1, 'kernel': '72.d1.b1', 'kernel_order': 24, 'label': '1728.46354.4h', 'nt': [12, 38], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234762
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 48, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '72.23', 'image_order': 72, 'indicator': 1, 'kernel': '72.d1.a1', 'kernel_order': 24, 'label': '1728.46354.4i', 'nt': [12, 38], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234763
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 24, 'counter': 48, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.d1.a1', 'kernel_order': 12, 'label': '1728.46354.4j1', 'nt': [24, 204], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234764
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 24, 'counter': 49, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.d1.a1', 'kernel_order': 12, 'label': '1728.46354.4j2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234766
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 50, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.c1.a1', 'kernel_order': 12, 'label': '1728.46354.4k1', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 38234767
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 51, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.c1.a1', 'kernel_order': 12, 'label': '1728.46354.4k2', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 38234768
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 52, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 12, 'label': '1728.46354.6a', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234769
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  • id: 38234770
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 54, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '192.1472', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 9, 'label': '1728.46354.6c', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234771
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  • id: 38234772
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 12, 'label': '1728.46354.6e', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234773
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 12, 'label': '1728.46354.6f', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234774
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.46354.6g', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234775
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 59, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.46354.6h', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234777
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 60, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.46354.6i', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234778
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 61, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.46354.6j', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234779
    {'center': '288.b1.a1', 'center_index': 288, 'center_order': 6, 'counter': 62, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8354', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.46354.6k1', 'nt': [36, 771], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234780
    {'center': '288.b1.a1', 'center_index': 288, 'center_order': 6, 'counter': 63, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8354', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.46354.6k2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234781
    {'center': '288.b1.a1', 'center_index': 288, 'center_order': 6, 'counter': 64, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8354', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.46354.6l1', 'nt': [36, 771], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234782
    {'center': '288.b1.a1', 'center_index': 288, 'center_order': 6, 'counter': 65, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8354', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.46354.6l2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234783
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8313', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.46354.6m1', 'nt': [36, 800], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234784
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8313', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.46354.6m2', 'nt': [36, 800], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234785
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8313', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.46354.6n1', 'nt': [36, 800], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234786
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8313', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.46354.6n2', 'nt': [36, 800], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234788
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 70, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '216.162', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.46354.8a', 'nt': [12, 117], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234789
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 71, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '432.598', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.46354.8b', 'nt': [24, 1295], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234790
    {'center': '864.a1.a1', 'center_index': 864, 'center_order': 2, 'counter': 72, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.46354.12a', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234791
    {'center': '864.a1.a1', 'center_index': 864, 'center_order': 2, 'counter': 73, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.46354.12b', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234792
    {'center': '864.a1.a1', 'center_index': 864, 'center_order': 2, 'counter': 74, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.46354', 'image_order': 1728, 'indicator': 1, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.46354.12c', 'nt': [36, 2466], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38234793
    {'center': '864.a1.a1', 'center_index': 864, 'center_order': 2, 'counter': 75, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '1728.46354', 'group_counter': 46354, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.46354', 'image_order': 1728, 'indicator': 1, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.46354.12d', 'nt': [36, 2466], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 264335838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1728, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1728.46354.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46354', 'subgroup_hash': 46354, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 264336101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 864, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4193', 'subgroup_hash': 4193, 'subgroup_order': 864, 'subgroup_tex': 'A_4\\times C_3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4172', 'subgroup_hash': 4172, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, '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': '864.4691', 'subgroup_hash': 4691, 'subgroup_order': 864, 'subgroup_tex': 'C_6:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 864, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, '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': '864.4137', 'subgroup_hash': 4137, 'subgroup_order': 864, 'subgroup_tex': 'C_3:C_{12}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.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': '864.4183', 'subgroup_hash': 4183, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.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': '864.4169', 'subgroup_hash': 4169, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': '576.8354', 'subgroup_hash': 8354, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 264335839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '576.7108', 'subgroup_hash': 7108, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264335950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '576.8313', 'subgroup_hash': 8313, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 432, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 264336035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 432, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 432, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.762', 'subgroup_hash': 762, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.624', 'subgroup_hash': 624, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.618', 'subgroup_hash': 618, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.4.h1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 288, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.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': '288.974', 'subgroup_hash': 974, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.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': '288.853', 'subgroup_hash': 853, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 264336179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '288.974', 'subgroup_hash': 974, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.551', 'subgroup_hash': 551, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.557', 'subgroup_hash': 557, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.626', 'subgroup_hash': 626, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.564', 'subgroup_hash': 564, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.559', 'subgroup_hash': 559, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.928', 'subgroup_hash': 928, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.920', 'subgroup_hash': 920, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1.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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1.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': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1.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': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1.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': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.u1.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': '288.705', 'subgroup_hash': 705, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.v1.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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.w1.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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.x1.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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.y1.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': '288.897', 'subgroup_hash': 897, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.z1.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': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.ba1.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': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bb1.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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bc1.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': '288.626', 'subgroup_hash': 626, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bd1.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': '288.855', 'subgroup_hash': 855, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 264336479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.be1.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': '288.855', 'subgroup_hash': 855, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 264336490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.6.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bf1.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': '288.909', 'subgroup_hash': 909, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 216, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 216, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.132', 'subgroup_hash': 132, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, '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': '192.1360', 'subgroup_hash': 1360, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, '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': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, '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': '192.1108', 'subgroup_hash': 1108, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 144, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 144, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 144, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 144, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 144, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 144, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.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': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.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': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.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': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.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': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.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': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.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': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264335840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.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': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1.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': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.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': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.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': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.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': '144.76', 'subgroup_hash': 76, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.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': '144.78', 'subgroup_hash': 78, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264335951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.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': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 264335962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1.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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264335973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1.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': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264335984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264335995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1.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': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 264336010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.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': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1.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': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.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': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.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': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.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': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.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': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.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': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 264336027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.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': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ck1.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': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cl1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cm1.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cn1.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cn1.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.co1.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': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.co1.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': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cp1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cp1.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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cq1.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cq1.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cr1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cr1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cs1.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': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cs1.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': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ct1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ct1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cu1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cu1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cv1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cv1.a2', '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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cv1.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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.12.cv1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cv1.b2', '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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '96.81', 'subgroup_hash': 81, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.q1.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': 18, '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': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.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': 18, '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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.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': 18, '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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.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': 18, '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': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.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': 18, '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': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.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': 18, '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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.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': 18, '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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.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': 18, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.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': 18, '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': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1.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': 18, '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': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ba1.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': 18, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bb1.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': 18, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bc1.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': 18, '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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bd1.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': 18, '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': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.be1.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': 18, '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': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bf1.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': 18, '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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bg1.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': 18, '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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bh1.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': 18, '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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 264336107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bi1.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': 18, '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': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bj1.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': 18, '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': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bk1.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': 18, '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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bl1.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': 18, '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': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bm1.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': 18, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.18.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bn1.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': 18, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 210, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': ['F', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 72, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 72, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 72, 'counter': 213, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1728.46354.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 214, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 215, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 216, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1.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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1.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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1.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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1.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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1.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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1.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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1.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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1.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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.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': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.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': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1.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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1.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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1.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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1.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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1.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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.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': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.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': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1.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': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1.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': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1.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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1.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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.da1.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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.da1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.da1.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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1.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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.db1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1.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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1.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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1.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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.de1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.a2', '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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1.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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1.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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1.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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1.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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1.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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dp1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1.a2', '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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.24.dq1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1.a2', '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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1728.46354.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 2}
  • id: 264336238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 48, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336249
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, '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': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336260
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.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': 36, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.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': 36, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336273
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.z1.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': 36, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ba1.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': 36, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bc1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1.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': 36, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1.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': 36, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1.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': 36, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1.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': 36, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1.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': 36, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1.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': 36, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1.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': 36, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1.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': 36, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1.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': 36, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336311
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ci1.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': 36, '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': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1.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': 36, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ck1.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': 36, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cl1.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': 36, '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': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1.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': 36, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1.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': 36, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.co1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cp1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cq1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1.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': 36, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1.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': 36, '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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cv1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dd1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.de1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.df1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dg1.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': 36, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dh1.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': 36, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.di1.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': 36, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dj1.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': 36, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dk1.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': 36, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dl1.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': 36, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1.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': 36, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dp1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dq1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ds1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dt1.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': 36, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.du1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1.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': 36, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dw1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dw1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dx1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dx1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dy1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dy1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dz1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dz1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ea1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.a2', '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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ea1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.b2', '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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.eb1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.eb1.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': 36, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ec1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ec1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ed1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ed1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ee1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ee1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ef1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ef1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eg1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eg1.a2', '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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eg1.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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eg1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eg1.b2', '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': 36, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eh1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.36.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eh1.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': 36, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 36, 'counter': 457, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 36, 'counter': 458, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 36, 'counter': 459, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 460, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 461, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 462, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336460
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336464
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336470
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336471
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336474
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336475
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cr1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336477
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336478
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.48.cr1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 264336495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1728.46354.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 264336497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 24, 'counter': 556, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 24, 'counter': 557, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 558, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 559, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1728.46354.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 560, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1728.46354.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336516
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1.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': 72, '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: 264336524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.x1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.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': 72, '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: 264336526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1.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': 72, '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: 264336527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ba1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1.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': 72, '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: 264336529
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1.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': 72, '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: 264336530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bd1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.be1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bf1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bg1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1.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': 72, '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: 264336536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bi1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1.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': 72, '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: 264336538
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bk1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.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': 72, '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: 264336540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bm1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bq1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bs1.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': 72, '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: 264336549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1.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': 72, '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: 264336550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.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': 72, '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: 264336551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.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': 72, '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: 264336552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1.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': 72, '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: 264336553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.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': 72, '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: 264336554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cc1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.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': 72, '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: 264336569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1.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': 72, '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: 264336570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cn1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1.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': 72, '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: 264336575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1.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': 72, '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: 264336576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1.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': 72, '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: 264336577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1.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': 72, '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: 264336578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1.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': 72, '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: 264336584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1.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': 72, '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: 264336585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1.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': 72, '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: 264336587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1.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': 72, '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: 264336588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1.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': 72, '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: 264336589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dj1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1.a2', '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1.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': 72, '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: 264336603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1.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': 72, '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: 264336605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ds1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.du1.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': 72, '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: 264336609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.du1.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': 72, '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: 264336610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dv1.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': 72, '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: 264336611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dv1.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': 72, '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: 264336613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dw1.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': 72, '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: 264336614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dw1.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': 72, '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: 264336615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dx1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.dz1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1.a2', '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ea1.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': 72, '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: 264336620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1.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': 72, '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: 264336621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1.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': 72, '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: 264336622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1.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': 72, '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: 264336624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1.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': 72, '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: 264336625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ee1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1.a2', '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': 72, '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: 264336626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ef1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ef1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.eg1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.eg1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ei1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ej1.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': 72, '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: 264336636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ej1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ej1.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': 72, '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: 264336637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1.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': 72, '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: 264336638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ek1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1.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': 72, '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: 264336639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.el1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.em1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.en1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1.a2', '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.en1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.en1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1.b2', '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1.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': 72, '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: 264336649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1.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': 72, '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: 264336650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1.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': 72, '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: 264336651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ep1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1.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': 72, '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: 264336652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1.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': 72, '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: 264336653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eq1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1.a2', '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': 72, '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: 264336654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1.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': 72, '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: 264336655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eq1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1.b2', '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': 72, '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: 264336658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.er1.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': 72, '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: 264336659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.er1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.er1.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': 72, '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: 264336660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.es1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.et1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.eu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ev1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1.a2', '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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ev1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1.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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ev1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1.b2', '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': 72, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ew1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ex1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ey1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1.a2', '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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ey1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1.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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ey1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1.b2', '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': 72, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ez1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fd1.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': 72, '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: 264336685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fd1.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': 72, '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: 264336686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fe1.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': 72, '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: 264336687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fe1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fe1.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': 72, '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: 264336688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ff1.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': 72, '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: 264336689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ff1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ff1.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': 72, '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: 264336691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1.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': 72, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fj1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1.a2', '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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fk1.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': 72, '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: 264336697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1.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': 72, '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: 264336698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fm1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1.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': 72, '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: 264336702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fp1.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': 72, '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: 264336703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1.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': 72, '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: 264336704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fq1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1.a2', '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': 72, '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: 264336705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fr1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fs1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.ft1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ft1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1.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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.72.fu1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1.a2', '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': 72, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 18, 'counter': 748, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336730
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.u1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bg1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.96.bh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264336755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 264336757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 264336764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.r1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.t1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.v1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.z1.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': 108, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ba1.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': 108, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bb1.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': 108, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bc1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 264336788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bd1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.be1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 264336791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bf1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bg1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bh1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bi1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bj1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bk1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bl1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bm1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bn1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bn1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bo1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bo1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bp1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bp1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bq1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.108.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bq1.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 836, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336809
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 837, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264336810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 838, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 839, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.153', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 153, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_6', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 12, 'counter': 840, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.151', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 151, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 264336826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.r1.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': 144, '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: 264336828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.v1.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': 144, '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: 264336832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.y1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336847
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1.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': 144, '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: 264336848
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1.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': 144, '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: 264336849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 873, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bl1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336850
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 874, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bm1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 875, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bn1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 876, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bo1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336853
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1.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': 144, '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: 264336854
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bq1.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': 144, '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: 264336855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 879, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.br1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bs1.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': 144, '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: 264336858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bt1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bu1.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': 144, '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: 264336860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bv1.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': 144, '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: 264336861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bw1.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': 144, '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: 264336862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bx1.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': 144, '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: 264336863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.by1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cb1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cc1.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': 144, '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: 264336870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ce1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cf1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ch1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cj1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336877
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ck1.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': 144, '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: 264336880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 900, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cl1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cm1.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': 144, '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: 264336882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cn1.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': 144, '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: 264336883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.co1.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': 144, '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: 264336884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cp1.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': 144, '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: 264336885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cq1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cr1.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': 144, '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: 264336887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cr1.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': 144, '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: 264336888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cs1.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': 144, '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: 264336889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cs1.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': 144, '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: 264336891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ct1.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': 144, '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: 264336892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ct1.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': 144, '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: 264336893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cu1.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': 144, '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: 264336894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cv1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cw1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cx1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cy1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cz1.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': 144, '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: 264336900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.da1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dd1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.de1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.df1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336910
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 928, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dh1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336911
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 929, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dh1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336913
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 930, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.di1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336914
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dj1.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': 144, '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: 264336915
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 932, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dk1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336916
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 933, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dk1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336917
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dl1.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': 144, '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: 264336918
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dm1.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': 144, '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: 264336919
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 936, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dn1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336920
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 937, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dn1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264336921
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.do1.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': 144, '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: 264336922
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.do1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.do1.a2', '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': 144, '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: 264336924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dp1.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': 144, '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: 264336925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dq1.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': 144, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dr1.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': 144, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ds1.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': 144, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264336928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dt1.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': 144, '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: 264336929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dt1.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': 144, '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: 264336930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dw1.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': 144, '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: 264336936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dw1.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': 144, '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: 264336937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ea1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ea1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1.b2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ed1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1.a2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ed1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1.b2', '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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.144.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264336959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 9, 'counter': 972, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1472', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1472, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 264336966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 8, 'counter': 979, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 264336983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.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': 216, '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: 264336985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1.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': 216, '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: 264336986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.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': 216, '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: 264336987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264336988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1.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': 216, '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: 264335843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1.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': 216, '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: 264335844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1.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': 216, '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: 264335845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.z1.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': 216, '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: 264335846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ba1.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': 216, '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: 264335847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bb1.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': 216, '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: 264335848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bc1.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': 216, '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: 264335849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bd1.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': 216, '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: 264335850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.be1.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': 216, '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: 264335852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bf1.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': 216, '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: 264335853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bg1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bh1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bi1.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': 216, '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: 264335856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bj1.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': 216, '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: 264335857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bk1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bl1.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': 216, '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: 264335859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bl1.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': 216, '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: 264335860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bm1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bn1.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': 216, '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: 264335863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bo1.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': 216, '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: 264335864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bp1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335865
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bp1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bq1.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': 216, '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: 264335867
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bq1.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': 216, '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: 264335868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1.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': 216, '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: 264335869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1.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': 216, '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: 264335870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bs1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bs1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bt1.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': 216, '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: 264335874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bt1.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': 216, '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: 264335875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bu1.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': 216, '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: 264335876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bu1.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': 216, '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: 264335877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bv1.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': 216, '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: 264335878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bv1.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': 216, '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: 264335879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bw1.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': 216, '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: 264335880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bw1.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': 216, '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: 264335881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bx1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.by1.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': 216, '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: 264335883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.by1.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': 216, '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: 264335885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bz1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 264335886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ca1.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': 216, '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: 264335887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.216.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cb1.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': 216, '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: 264335888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1043, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.46354.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264335889
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1044, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.46354.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264335890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1045, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 264335891
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1046, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 264335892
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 1047, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 264335893
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 1048, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335894
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 1049, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335896
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1050, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335897
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1051, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335898
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1052, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335899
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1053, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335900
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1054, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335901
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1055, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335902
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1056, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335903
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1057, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335904
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1058, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, '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: 264335905
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.q1.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': 288, '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: 264335907
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1060, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.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': 288, '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: 264335908
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1061, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.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': 288, '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: 264335909
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1062, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.s1.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': 288, '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: 264335910
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1063, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.s1.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': 288, '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: 264335911
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1064, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.t1.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': 288, '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: 264335912
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1065, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.t1.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': 288, '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: 264335913
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.u1.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': 288, '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: 264335914
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.u1.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': 288, '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: 264335915
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1068, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.v1.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': 288, '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: 264335916
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.w1.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': 288, '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: 264335918
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1070, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.x1.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': 288, '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: 264335919
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.y1.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': 288, '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: 264335920
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.z1.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': 288, '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: 264335921
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ba1.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': 288, '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: 264335922
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.ba1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ba1.a2', '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': 288, '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: 264335923
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1075, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bb1.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': 288, '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: 264335924
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bc1.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': 288, '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: 264335925
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bd1.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': 288, '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: 264335926
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.be1.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': 288, '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: 264335927
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bf1.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': 288, '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: 264335929
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bg1.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': 288, '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: 264335930
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1.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': 288, '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: 264335931
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1.a2', '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': 288, '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: 264335932
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bi1.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': 288, '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: 264335933
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bj1.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': 288, '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: 264335934
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1.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': 288, '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: 264335935
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bk1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1.a2', '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': 288, '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: 264335936
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bl1.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': 288, '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: 264335937
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bm1.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': 288, '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: 264335938
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bn1.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': 288, '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: 264335940
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bo1.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': 288, '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: 264335941
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.288.bo1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bo1.a2', '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': 288, '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: 264335942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 4, 'counter': 1092, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46354.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.598', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 598, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 264335943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 2, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 264335944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 264335945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 264335946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, '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: 264335947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335953
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335955
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 264335960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.q1.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': 432, '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: 264335961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.r1.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': 432, '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: 264335963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.s1.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': 432, '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: 264335964
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.t1.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': 432, '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: 264335965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.u1.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': 432, '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: 264335966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.v1.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': 432, '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: 264335967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.w1.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': 432, '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: 264335968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.w1.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': 432, '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: 264335969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.x1.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': 432, '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: 264335970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.y1.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': 432, '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: 264335971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.z1.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': 432, '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: 264335972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ba1.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': 432, '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: 264335974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bb1.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': 432, '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: 264335975
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bc1.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': 432, '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: 264335976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bc1.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': 432, '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: 264335977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bd1.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': 432, '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: 264335978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.432.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be1.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': 432, '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: 264335979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bf1.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': 432, '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: 264335980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bf1.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': 432, '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: 264335981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bg1.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': 432, '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: 264335982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bg1.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': 432, '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: 264335983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bh1.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': 432, '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: 264335985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bh1.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': 432, '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: 264335986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bi1.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': 432, '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: 264335987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.46354.432.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bi1.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': 432, '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: 264335988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 1133, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.46354.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8313', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8313, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times D_{12}', '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': 0}
  • id: 264335989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 1134, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.46354.576.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8354', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8354, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_3^2', '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': 0}
  • id: 264335990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.576.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264335991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 1136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.576.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264335992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1137, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.576.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264335993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.576.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264335994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.576.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264335996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 1140, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.46354.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.4673', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4673, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0'], '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: 264335997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 264335998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 264335999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 264336000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 264336001
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 264336002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 264336003
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 264336004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 264336005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 264336007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1150, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.46354.864.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 264336008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.46354', 'ambient_counter': 46354, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 1, 'counter': 1151, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1728.46354.1728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1728.46354', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46354, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3.S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C8'], '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: 264335838
    {'ambient': '1728.46354', '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': '864.a1.a1', 'complements': ['1728.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '4.h1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6656, 4470, 4570, 5228, 2445, 4618, 3419, 4572], 'generators': [46999, 70633, 1341703, 622537, 1674451, 793169, 887131, 622105, 835777], 'label': '1728.46354.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '864.4673', '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': '864.4673'}
  • id: 264335839
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '6.o1.a1', '6.q1.a1', '6.t1.a1', '6.u1.a1', '6.bb1.a1', '6.bc1.a1', '9.a1.a1', '9.c1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3506, -1, 6659, -1, 5696, -1, 6340, -1], 'generators': [46999, 793169, 887131, 1674451, 70633, 622105, 622537, 835777], 'label': '1728.46354.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335840
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.bb1.a1'], 'contains': ['24.j1.a1', '24.r1.a1', '24.s1.a1', '36.bo1.a1', '36.bq1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3932, -1, 7779, -1, 6657, -1, 7104, -1], 'generators': [812125, 622105, 622537, 1634131, 1633643, 887131], 'label': '1728.46354.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264335841
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1.a1', '72.ci1.a1', '72.cj1.a1', '108.h1.a1', '108.bk1.a1', '108.bm1.a1'], 'contains': ['432.d1.a1', '432.h1.a1', '432.i1.a1', '432.bi1.a1', '432.bi1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [832, -1, 8817, -1, 7873, -1, 8171, -1], 'generators': [46999, 793657, 793169], 'label': '1728.46354.216.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335842
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1.a1', '72.cm1.a1', '72.cp1.a1', '108.j1.a1', '108.bj1.a1', '108.bm1.a1'], 'contains': ['432.d1.a1', '432.j1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [899, -1, 6925, -1, 7130, -1, 7328, -1], 'generators': [46999, 835777], 'label': '1728.46354.216.w1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335843
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1.a1', '72.cn1.a1', '108.j1.a1', '108.bk1.a1', '108.bl1.a1'], 'contains': ['432.d1.a1', '432.k1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [774, -1, 9266, -1, 8002, -1, 8115, -1], 'generators': [46999, 1674955], 'label': '1728.46354.216.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335844
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cq1.a1', '72.cu1.a1', '108.b1.a1', '108.l1.a1', '108.bl1.a1'], 'contains': ['432.e1.a1', '432.f1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1838, -1, 8852, -1, 7572, -1, 7707, -1], 'generators': [835273, 1674955], 'label': '1728.46354.216.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335845
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cr1.a1', '72.cv1.a1', '108.b1.a1', '108.n1.a1', '108.bm1.a1'], 'contains': ['432.e1.a1', '432.h1.a1', '432.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [817, -1, 8579, -1, 7758, -1, 7821, -1], 'generators': [835273, 835777], 'label': '1728.46354.216.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335846
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cs1.a1', '72.cw1.a1', '108.c1.a1', '108.l1.a1', '108.n1.a1'], 'contains': ['432.e1.a1', '432.h1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1818, -1, 8084, -1, 7233, -1, 7351, -1], 'generators': [1651771, 1674955], 'label': '1728.46354.216.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1.a1', 'old_label': '216.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335847
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1.a1', '72.cx1.a1', '108.d1.a1', '108.bl1.a1', '108.bm1.a1'], 'contains': ['432.e1.a1', '432.i1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [545, -1, 9232, -1, 7950, -1, 8043, -1], 'generators': [834823, 835273], 'label': '1728.46354.216.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335848
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1.a1', '72.cz1.a1', '72.da1.a1', '108.q1.a1', '108.bj1.a1', '108.bl1.a1'], 'contains': ['432.f1.a1', '432.g1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1858, -1, 7407, -1, 7158, -1, 7304, -1], 'generators': [834823, 1634131], 'label': '1728.46354.216.bc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335849
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1.a1', '72.de1.a1', '108.q1.a1', '108.bk1.a1', '108.bm1.a1'], 'contains': ['432.g1.a1', '432.h1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [795, -1, 8835, -1, 8049, -1, 8154, -1], 'generators': [834823, 793657], 'label': '1728.46354.216.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335850
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1.a1', '72.df1.a1', '72.dh1.a1', '72.di1.a1', '108.u1.a1', '108.bj1.a1', '108.bm1.a1'], 'contains': ['432.g1.a1', '432.i1.a1', '432.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1538, -1, 7396, -1, 7040, -1, 7258, -1], 'generators': [1675405, 835777], 'label': '1728.46354.216.be1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335851
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.k1.a1', '6.bb1.a1'], 'contains': ['24.k1.a1', '24.l1.a1', '24.s1.a1', '24.ci1.a1', '36.bs1.a1', '36.bv1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3057, -1, 8057, -1, 7722, -1, 7730, -1], 'generators': [812125, 622105, 622537, 1656811, 887131, 1633643], 'label': '1728.46354.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335852
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1.a1', '72.dg1.a1', '108.u1.a1', '108.bk1.a1', '108.bl1.a1'], 'contains': ['432.g1.a1', '432.i1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [856, -1, 9249, -1, 8030, -1, 8138, -1], 'generators': [1675405, 1674955], 'label': '1728.46354.216.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335853
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1.a1', '72.dk1.a1', '108.a1.a1'], 'contains': ['432.m1.a1', '432.n1.a1', '432.q1.a1', '432.bf1.a1', '432.bf1.b1', '432.bg1.a1', '432.bg1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3444, -1, 9769, -1, 8358, -1, 8681, -1], 'generators': [46999, 1674451, 1633643], 'label': '1728.46354.216.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '216.bg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335854
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1.a1', '72.dm1.a1', '72.dn1.a1', '72.dn1.a2', '108.h1.a1'], 'contains': ['432.n1.a1', '432.p1.a1', '432.s1.a1', '432.bh1.a1', '432.bh1.b1', '432.bi1.a1', '432.bi1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2244, -1, 8355, -1, 7593, -1, 7725, -1], 'generators': [46999, 1634131, 1633643], 'label': '1728.46354.216.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '216.bh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335855
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.do1.a1', '72.dp1.a1', '108.o1.a1'], 'contains': ['432.o1.a1', '432.s1.a1', '432.t1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1734, -1, 9125, -1, 8161, -1, 8332, -1], 'generators': [812125, 1651771], 'label': '1728.46354.216.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1.a1', 'old_label': '216.bi1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335856
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dq1.a1', '72.dr1.a1', '108.t1.a1'], 'contains': ['432.q1.a1', '432.r1.a1', '432.t1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2788, -1, 9142, -1, 8204, -1, 8429, -1], 'generators': [812125, 1656811], 'label': '1728.46354.216.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1.a1', 'old_label': '216.bj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335857
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ds1.a1', '72.dt1.a1', '108.bc1.a1', '108.bn1.a1', '108.bn1.b1'], 'contains': ['432.m1.a1', '432.o1.a1', '432.u1.a1', '432.v1.a1', '432.x1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5387, -1, 5287, -1, 4927, -1, 5492, -1], 'generators': [1674451, 817145, 887131], 'label': '1728.46354.216.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335858
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1.a1', '72.dv1.a1', '72.dw1.a1', '108.bd1.a1', '108.bn1.a1', '108.bo1.a1'], 'contains': ['432.u1.a1', '432.w1.a1', '432.bc1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6201, -1, 4256, -1, 4116, -1, 4395, -1], 'generators': [46999, 817145], 'label': '1728.46354.216.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.bl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335859
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1.b1', '72.dv1.b1', '72.dw1.b1', '108.bd1.a1', '108.bn1.b1', '108.bo1.b1'], 'contains': ['432.u1.a1', '432.w1.b1', '432.bc1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6201, -1, 4302, -1, 4116, -1, 4411, -1], 'generators': [70957, 817145], 'label': '1728.46354.216.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.bl1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335860
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dx1.a1', '72.dy1.a1', '72.dz1.a1', '72.dz1.a2', '108.be1.a1', '108.bo1.a1', '108.bo1.b1'], 'contains': ['432.p1.a1', '432.r1.a1', '432.u1.a1', '432.y1.a1', '432.ba1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5284, -1, 3593, -1, 4016, -1, 3722, -1], 'generators': [1634131, 817145, 887131], 'label': '1728.46354.216.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335861
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ea1.a1', '72.eb1.a1', '108.bf1.a1', '108.bn1.a1', '108.bn1.b1'], 'contains': ['432.u1.a1', '432.z1.a1', '432.bd1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6285, -1, 5129, -1, 4732, -1, 5219, -1], 'generators': [1675405, 817145], 'label': '1728.46354.216.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335862
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.k1.a1', '6.bc1.a1'], 'contains': ['24.k1.a1', '24.m1.a1', '24.n1.a1', '24.ca1.a1', '24.cb1.a1', '36.bt1.a1', '36.bw1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1896, -1, 7874, -1, 8135, -1, 8322, -1], 'generators': [1675405, 622105, 622537, 835777, 887131, 793169], 'label': '1728.46354.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264335863
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ec1.a1', '72.ed1.a1', '72.ee1.a1', '72.ee1.a2', '108.bg1.a1', '108.bo1.a1', '108.bo1.b1'], 'contains': ['432.u1.a1', '432.bb1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5691, -1, 3170, -1, 3517, -1, 3458, -1], 'generators': [1633789, 817145], 'label': '1728.46354.216.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335864
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ef1.a1', '72.eh1.a1', '108.a1.a1', '108.bn1.a1', '108.bp1.a1'], 'contains': ['432.v1.a1', '432.w1.a1', '432.z1.a1', '432.bf1.a1', '432.bg1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6841, -1, 5300, -1, 5267, -1, 5597, -1], 'generators': [46999, 1674451, 887131], 'label': '1728.46354.216.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335865
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ef1.b1', '72.eh1.b1', '108.a1.a1', '108.bn1.b1', '108.bp1.b1'], 'contains': ['432.v1.a1', '432.w1.b1', '432.z1.a1', '432.bf1.b1', '432.bg1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6841, -1, 4912, -1, 5267, -1, 5662, -1], 'generators': [793511, 1674451, 887131], 'label': '1728.46354.216.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bp1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335866
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eg1.a1', '72.ei1.a1', '108.e1.a1', '108.bn1.b1', '108.bp1.a1'], 'contains': ['432.v1.a1', '432.bc1.a1', '432.bd1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7099, -1, 4832, -1, 4533, -1, 5185, -1], 'generators': [70957, 1674451], 'label': '1728.46354.216.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335867
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eg1.b1', '72.ei1.b1', '108.e1.a1', '108.bn1.a1', '108.bp1.b1'], 'contains': ['432.v1.a1', '432.bc1.b1', '432.bd1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7099, -1, 4894, -1, 4533, -1, 4956, -1], 'generators': [817469, 1674451], 'label': '1728.46354.216.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335868
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1.a1', '72.ek1.a1', '108.g1.a1', '108.bn1.a1', '108.bp1.a1'], 'contains': ['432.w1.a1', '432.x1.a1', '432.bd1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7078, -1, 5207, -1, 4564, -1, 4916, -1], 'generators': [46999, 1651771], 'label': '1728.46354.216.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.br1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335869
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1.b1', '72.ek1.b1', '108.g1.a1', '108.bn1.b1', '108.bp1.b1'], 'contains': ['432.w1.b1', '432.x1.a1', '432.bd1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7078, -1, 4872, -1, 4564, -1, 5238, -1], 'generators': [793511, 1651771], 'label': '1728.46354.216.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.br1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335870
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1.a1', '72.em1.a1', '72.en1.a1', '72.en1.a2', '108.h1.a1', '108.bo1.a1', '108.bq1.a1'], 'contains': ['432.w1.a1', '432.y1.a1', '432.bb1.a1', '432.bh1.a1', '432.bi1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5807, -1, 3276, -1, 4037, -1, 3778, -1], 'generators': [46999, 1634131, 887131], 'label': '1728.46354.216.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335871
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1.b1', '72.em1.b1', '72.en1.b1', '72.en1.b2', '108.h1.a1', '108.bo1.b1', '108.bq1.b1'], 'contains': ['432.w1.b1', '432.y1.a1', '432.bb1.a1', '432.bh1.b1', '432.bi1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5807, -1, 3772, -1, 4037, -1, 3740, -1], 'generators': [793511, 1634131, 887131], 'label': '1728.46354.216.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bs1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335872
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eo1.a1', '72.ep1.a1', '72.eq1.a1', '72.eq1.a2', '108.i1.a1', '108.bo1.a1', '108.bq1.a1'], 'contains': ['432.w1.a1', '432.ba1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5732, -1, 3461, -1, 3735, -1, 3638, -1], 'generators': [46999, 1656811], 'label': '1728.46354.216.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bt1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335873
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '6.bc1.a1'], 'contains': ['24.k1.a1', '24.p1.a1', '24.t1.a1', '36.bu1.a1', '36.bx1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3146, -1, 7746, -1, 7078, -1, 7282, -1], 'generators': [1675405, 622105, 622537, 811801, 1633643, 887131], 'label': '1728.46354.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335874
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eo1.b1', '72.ep1.b1', '72.eq1.b1', '72.eq1.b2', '108.i1.a1', '108.bo1.b1', '108.bq1.b1'], 'contains': ['432.w1.b1', '432.ba1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5732, -1, 3701, -1, 3735, -1, 3622, -1], 'generators': [793511, 1656811], 'label': '1728.46354.216.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bt1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335875
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.er1.a1', '72.es1.a1', '108.m1.a1', '108.bn1.b1', '108.bp1.a1'], 'contains': ['432.x1.a1', '432.z1.a1', '432.bc1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7010, -1, 4860, -1, 4628, -1, 5332, -1], 'generators': [70957, 1651771], 'label': '1728.46354.216.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335876
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.er1.b1', '72.es1.b1', '108.m1.a1', '108.bn1.a1', '108.bp1.b1'], 'contains': ['432.x1.a1', '432.z1.a1', '432.bc1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7010, -1, 5235, -1, 4628, -1, 5014, -1], 'generators': [817469, 1651771], 'label': '1728.46354.216.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.bu1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335877
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.et1.a1', '72.eu1.a1', '72.ev1.a1', '72.ev1.a2', '108.r1.a1', '108.bo1.b1', '108.bq1.a1'], 'contains': ['432.y1.a1', '432.bc1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5898, -1, 3525, -1, 3627, -1, 3482, -1], 'generators': [70957, 1634131], 'label': '1728.46354.216.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335878
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.et1.b1', '72.eu1.b1', '72.ev1.b1', '72.ev1.b2', '108.r1.a1', '108.bo1.a1', '108.bq1.b1'], 'contains': ['432.y1.a1', '432.bc1.b1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5898, -1, 3217, -1, 3627, -1, 3661, -1], 'generators': [817469, 1634131], 'label': '1728.46354.216.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bv1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335879
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ew1.a1', '72.ex1.a1', '72.ey1.a1', '72.ey1.a2', '108.w1.a1', '108.bo1.b1', '108.bq1.a1'], 'contains': ['432.ba1.a1', '432.bb1.a1', '432.bc1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6020, -1, 3641, -1, 3716, -1, 3521, -1], 'generators': [70957, 1656811], 'label': '1728.46354.216.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335880
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ew1.b1', '72.ex1.b1', '72.ey1.b1', '72.ey1.b2', '108.w1.a1', '108.bo1.a1', '108.bq1.b1'], 'contains': ['432.ba1.a1', '432.bb1.a1', '432.bc1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6020, -1, 3258, -1, 3716, -1, 3684, -1], 'generators': [817469, 1656811], 'label': '1728.46354.216.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.bw1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335881
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ez1.a1', '72.fa1.a1', '72.fb1.a1', '72.fc1.a1', '108.bc1.a1', '108.bp1.a1', '108.bp1.b1'], 'contains': ['432.a1.a1', '432.v1.a1', '432.x1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8428, -1, 2306, -1, 3193, -1, 2910, -1], 'generators': [1674451, 887131, 70633], 'label': '1728.46354.216.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '216.bx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335882
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.fd1.a1', '72.fe1.a1', '72.ff1.a1', '108.bd1.a1', '108.bp1.a1', '108.bq1.a1'], 'contains': ['432.a1.a1', '432.w1.a1', '432.bc1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8089, -1, 2069, -1, 3000, -1, 2430, -1], 'generators': [46999, 70633], 'label': '1728.46354.216.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.by1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335883
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '72.fd1.b1', '72.fe1.b1', '72.ff1.b1', '108.bd1.a1', '108.bp1.b1', '108.bq1.b1'], 'contains': ['432.a1.a1', '432.w1.b1', '432.bc1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8089, -1, 2022, -1, 3000, -1, 2480, -1], 'generators': [793511, 70633], 'label': '1728.46354.216.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.by1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335884
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.k1.a1', '6.t1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.o1.a1', '24.cv1.a1', '24.cv1.b1', '36.by1.a1', '36.bz1.a1', '36.ca1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2354, -1, 6800, -1, 6003, -1, 5822, -1], 'generators': [70957, 622105, 622537, 1656811, 793169, 887131], 'label': '1728.46354.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335885
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1.a1', '72.fh1.a1', '72.fi1.a1', '72.fj1.a1', '72.fj1.a2', '108.be1.a1', '108.bq1.a1', '108.bq1.b1'], 'contains': ['432.a1.a1', '432.y1.a1', '432.ba1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7921, -1, 1720, -1, 2839, -1, 2227, -1], 'generators': [1634131, 887131, 70633], 'label': '1728.46354.216.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '216.bz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335886
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fk1.a1', '72.fl1.a1', '72.fm1.a1', '72.fn1.a1', '108.bf1.a1', '108.bp1.a1', '108.bp1.b1'], 'contains': ['432.a1.a1', '432.z1.a1', '432.bd1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8473, -1, 2252, -1, 3213, -1, 3150, -1], 'generators': [1675405, 70633], 'label': '1728.46354.216.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.ca1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335887
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fo1.a1', '72.fp1.a1', '72.fq1.a1', '72.fq1.a2', '72.fr1.a1', '72.fs1.a1', '72.ft1.a1', '72.fu1.a1', '72.fu1.a2', '108.bg1.a1', '108.bq1.a1', '108.bq1.b1'], 'contains': ['432.a1.a1', '432.bb1.a1', '432.be1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9084, -1, 1134, -1, 2696, -1, 1370, -1], 'generators': [1633789, 70633], 'label': '1728.46354.216.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '216.cb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264335888
    {'ambient': '1728.46354', 'aut_centralizer_order': 3456, 'aut_label': '288.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '144.b1.a1', '144.f1.a1', '144.i1.a1', '144.l1.a1', '144.p1.a1', '144.s1.a1', '144.v1.a1', '144.z1.a1', '144.bc1.a1', '144.bj1.a1', '144.bk1.a1'], 'contains': ['576.a1.a1', '864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1108, 5383, 8446, 4076, 7829, 5356, 7337, 4054], 'generators': [793169, 622105], 'label': '1728.46354.288.a1.a1', 'mobius_quo': 1, 'mobius_sub': 288, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.a1.a1', '144.b1.a1'], 'normal_contains': ['576.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335889
    {'ambient': '1728.46354', 'aut_centralizer_order': 3456, 'aut_label': '288.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.d1.a1', '96.e1.a1', '144.a1.a1', '144.g1.a1', '144.m1.a1', '144.q1.a1', '144.t1.a1', '144.w1.a1', '144.ba1.a1', '144.bd1.a1', '144.bl1.a1', '144.bm1.a1', '144.bn1.a1'], 'contains': ['576.b1.a1', '864.a1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1661, 6617, 8015, 3630, 7122, 6282, 8025, 4378], 'generators': [793169, 622537], 'label': '1728.46354.288.b1.a1', 'mobius_quo': 1, 'mobius_sub': 288, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['72.b1.a1', '96.a1.a1', '144.a1.a1'], 'normal_contains': ['576.b1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335890
    {'ambient': '1728.46354', 'aut_centralizer_order': 1728, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.f1.a1', '96.g1.a1', '144.h1.a1', '144.n1.a1', '144.u1.a1', '144.bb1.a1', '144.be1.a1'], 'contains': ['576.c1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5100, -1, 5411, -1, 5653, -1, 6377, -1], 'generators': [793169, 47089], 'label': '1728.46354.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '288.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335891
    {'ambient': '1728.46354', 'aut_centralizer_order': 864, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '96.b1.a1', '96.d1.a1', '96.f1.a1', '144.j1.a1', '144.o1.a1', '144.r1.a1', '144.x1.a1', '144.bf1.a1', '144.bo1.a1', '144.bp1.a1'], 'contains': ['576.d1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7374, -1, 2768, -1, 1803, -1, 1924, -1], 'generators': [793169, 1341703], 'label': '1728.46354.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '288.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335892
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1.a1', '96.b1.a1', '96.e1.a1', '96.g1.a1', '144.k1.a1', '144.bg1.a1', '144.bq1.a1'], 'contains': ['576.e1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7762, -1, 2214, -1, 1000, -1, 1197, -1], 'generators': [793169, 766291], 'label': '1728.46354.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '288.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335893
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.a1', '96.c1.a1', '96.d1.a1', '96.g1.a1', '144.y1.a1', '144.bh1.a1', '144.br1.a1'], 'contains': ['576.f1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8503, -1, 2436, -1, 1499, -1, 1998, -1], 'generators': [793169, 767155], 'label': '1728.46354.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '288.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335894
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.a1', '96.c1.a1', '96.e1.a1', '96.f1.a1', '96.g1.a1', '144.bi1.a1'], 'contains': ['576.g1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8737, -1, 1282, -1, 942, -1, 1074, -1], 'generators': [793169, 1342135], 'label': '1728.46354.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.f1.a1', 'old_label': '288.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335895
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.i1.a1', '6.bb1.a1'], 'contains': ['24.l1.a1', '24.q1.a1', '24.r1.a1', '36.cb1.a1', '36.cc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1936, -1, 6759, -1, 6577, -1, 6989, -1], 'generators': [834823, 622105, 622537, 1656811, 793169, 887131], 'label': '1728.46354.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335896
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '144.f1.a1', '144.bs1.a1', '144.bu1.a1', '144.bx1.a1', '144.bz1.a1', '144.cc1.a1', '144.ce1.a1', '144.ch1.a1', '144.ck1.a1', '144.cm1.a1'], 'contains': ['576.a1.a1', '864.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2606, -1, 9576, -1, 8387, -1, 7811, -1], 'generators': [1633643, 622105], 'label': '1728.46354.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.h1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335897
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '144.g1.a1', '144.bt1.a1', '144.bv1.a1', '144.by1.a1', '144.ca1.a1', '144.cd1.a1', '144.cf1.a1', '144.ci1.a1', '144.cl1.a1', '144.cn1.a1'], 'contains': ['576.b1.a1', '864.b1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2750, -1, 9171, -1, 7457, -1, 8707, -1], 'generators': [1633643, 622537], 'label': '1728.46354.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.i1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335898
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '144.h1.a1', '144.bw1.a1', '144.cb1.a1', '144.cb1.a2', '144.cg1.a1', '144.cj1.a1', '144.co1.a1'], 'contains': ['576.c1.a1', '864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4228, -1, 7036, -1, 7062, -1, 7015, -1], 'generators': [1633643, 47089], 'label': '1728.46354.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '288.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335899
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.c1.a1', '144.f1.a1', '144.cm1.a1', '144.cp1.a1', '144.cr1.a1', '144.cr1.b1', '144.cu1.a1', '144.cw1.a1', '144.cz1.a1', '144.db1.a1', '144.de1.a1', '144.dh1.a1', '144.dh1.b1', '144.di1.a1', '144.dj1.a1'], 'contains': ['576.a1.a1', '864.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6475, -1, 4552, -1, 4312, -1, 4559, -1], 'generators': [887131, 622105], 'label': '1728.46354.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.k1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335900
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.d1.a1', '144.g1.a1', '144.cn1.a1', '144.cq1.a1', '144.cs1.a1', '144.cs1.b1', '144.cv1.a1', '144.cx1.a1', '144.da1.a1', '144.dc1.a1', '144.df1.a1', '144.dk1.a1', '144.dk1.b1', '144.dl1.a1', '144.dm1.a1'], 'contains': ['576.b1.a1', '864.c1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6613, -1, 4656, -1, 4266, -1, 4613, -1], 'generators': [887131, 622537], 'label': '1728.46354.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.l1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335901
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.h1.a1', '144.co1.a1', '144.ct1.a1', '144.ct1.b1', '144.cy1.a1', '144.cy1.a2', '144.dd1.a1', '144.dd1.a2', '144.dg1.a1', '144.dg1.a2', '144.dn1.a1', '144.dn1.b1', '144.do1.a1', '144.do1.a2', '144.dp1.a1'], 'contains': ['576.c1.a1', '864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6765, -1, 3118, -1, 3589, -1, 3287, -1], 'generators': [887131, 47089], 'label': '1728.46354.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '288.m1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335902
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '96.k1.a1', '144.i1.a1', '144.bs1.a1', '144.cp1.a1', '144.dt1.a1', '144.dt1.b1'], 'contains': ['576.a1.a1', '864.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4971, -1, 7998, -1, 7438, -1, 7419, -1], 'generators': [1674451, 622105], 'label': '1728.46354.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '288.n1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335903
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fa1.a1', '96.j1.a1', '96.l1.a1', '144.j1.a1', '144.du1.a1', '144.du1.b1'], 'contains': ['576.d1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9357, -1, 1443, -1, 1518, -1, 1566, -1], 'generators': [1674451, 1341703], 'label': '1728.46354.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '288.o1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335904
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fb1.a1', '96.j1.a1', '96.m1.a1', '144.k1.a1'], 'contains': ['576.e1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9247, -1, 1271, -1, 962, -1, 1118, -1], 'generators': [1674451, 766291], 'label': '1728.46354.288.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.h1.a1', 'old_label': '288.p1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335905
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.l1.a1', '96.m1.a1', '144.a1.a1', '144.bt1.a1', '144.cq1.a1', '144.dv1.a1', '144.dv1.b1'], 'contains': ['576.b1.a1', '864.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5231, -1, 7705, -1, 6938, -1, 7776, -1], 'generators': [1674451, 622537], 'label': '1728.46354.288.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '288.q1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335906
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.bc1.a1'], 'contains': ['24.m1.a1', '24.p1.a1', '24.r1.a1', '36.cd1.a1', '36.ce1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2637, -1, 7354, -1, 6906, -1, 7217, -1], 'generators': [1651447, 622105, 622537, 811801, 1633643, 887131], 'label': '1728.46354.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264335907
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '96.o1.a1', '144.l1.a1', '144.bu1.a1', '144.cr1.a1', '144.dt1.a1', '144.dw1.a1', '144.dy1.a1', '144.eb1.a1'], 'contains': ['576.a1.a1', '864.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3714, -1, 8954, -1, 8114, -1, 7565, -1], 'generators': [46999, 622105], 'label': '1728.46354.288.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '288.r1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335908
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.b1', '96.o1.b1', '144.l1.a1', '144.bu1.a1', '144.cr1.b1', '144.dt1.b1', '144.dw1.b1', '144.dy1.b1', '144.eb1.b1'], 'contains': ['576.a1.a1', '864.e1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3714, -1, 8926, -1, 8114, -1, 7600, -1], 'generators': [793511, 622105], 'label': '1728.46354.288.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '288.r1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335909
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '96.p1.a1', '144.m1.a1', '144.bv1.a1', '144.cs1.a1', '144.dv1.a1', '144.dx1.a1', '144.dz1.a1', '144.ec1.a1'], 'contains': ['576.b1.a1', '864.e1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3728, -1, 8618, -1, 7265, -1, 8406, -1], 'generators': [46999, 622537], 'label': '1728.46354.288.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '288.s1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335910
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.b1', '96.p1.b1', '144.m1.a1', '144.bv1.a1', '144.cs1.b1', '144.dv1.b1', '144.dx1.b1', '144.dz1.b1', '144.ec1.b1'], 'contains': ['576.b1.a1', '864.e1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3728, -1, 8560, -1, 7265, -1, 8505, -1], 'generators': [793511, 622537], 'label': '1728.46354.288.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '288.s1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335911
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '96.q1.a1', '144.n1.a1', '144.bw1.a1', '144.ct1.a1', '144.ea1.a1', '144.ea1.a2', '144.ed1.a1', '144.ed1.a2'], 'contains': ['576.c1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5005, -1, 6000, -1, 5792, -1, 6947, -1], 'generators': [46999, 47089], 'label': '1728.46354.288.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '288.t1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335912
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.b1', '96.q1.b1', '144.n1.a1', '144.bw1.a1', '144.ct1.b1', '144.ea1.b1', '144.ea1.b2', '144.ed1.b1', '144.ed1.b2'], 'contains': ['576.c1.a1', '864.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5005, -1, 5967, -1, 5792, -1, 6999, -1], 'generators': [793511, 47089], 'label': '1728.46354.288.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '288.t1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335913
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '96.o1.a1', '96.p1.a1', '96.q1.a1', '144.o1.a1', '144.du1.a1', '144.ee1.a1'], 'contains': ['576.d1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9290, -1, 929, -1, 1344, -1, 1142, -1], 'generators': [46999, 1341703], 'label': '1728.46354.288.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '288.u1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335914
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '96.o1.b1', '96.p1.b1', '96.q1.b1', '144.o1.a1', '144.du1.b1', '144.ee1.b1'], 'contains': ['576.d1.a1', '864.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9290, -1, 838, -1, 1344, -1, 1158, -1], 'generators': [793511, 1341703], 'label': '1728.46354.288.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '288.u1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335915
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '144.p1.a1', '144.bs1.a1', '144.bx1.a1', '144.cp1.a1', '144.cu1.a1', '144.dw1.a1', '144.dw1.b1'], 'contains': ['576.a1.a1', '864.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3642, -1, 8056, -1, 8329, -1, 7827, -1], 'generators': [835273, 622105], 'label': '1728.46354.288.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '288.v1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335916
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '144.q1.a1', '144.bt1.a1', '144.by1.a1', '144.cq1.a1', '144.cv1.a1', '144.dx1.a1', '144.dx1.b1'], 'contains': ['576.b1.a1', '864.f1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3700, -1, 8033, -1, 7375, -1, 8723, -1], 'generators': [835273, 622537], 'label': '1728.46354.288.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '288.w1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335917
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.k1.a1', '6.u1.a1'], 'contains': ['24.n1.a1', '24.o1.a1', '24.s1.a1', '36.cf1.a1', '36.ci1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2081, -1, 7439, -1, 6981, -1, 7141, -1], 'generators': [70957, 622105, 887131, 835777, 622537, 793169], 'label': '1728.46354.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264335918
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '144.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1', '96.u1.a2', '144.r1.a1', '144.ee1.a1', '144.ee1.b1'], 'contains': ['576.d1.a1', '864.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8968, -1, 572, -1, 1261, -1, 956, -1], 'generators': [1634131, 1341703], 'label': '1728.46354.288.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.co1.a1', 'old_label': '288.x1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335919
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1.a1', '96.v1.a1', '144.s1.a1', '144.bz1.a1', '144.cw1.a1', '144.dy1.a1', '144.dy1.b1'], 'contains': ['576.a1.a1', '864.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3975, -1, 8737, -1, 7103, -1, 7172, -1], 'generators': [1634131, 622105], 'label': '1728.46354.288.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '288.y1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335920
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1.a1', '96.v1.a1', '144.t1.a1', '144.ca1.a1', '144.cx1.a1', '144.dz1.a1', '144.dz1.b1'], 'contains': ['576.b1.a1', '864.g1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4181, -1, 8364, -1, 6897, -1, 7460, -1], 'generators': [1634131, 622537], 'label': '1728.46354.288.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '288.z1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335921
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.u1.a1', '96.v1.a1', '144.u1.a1', '144.cb1.a1', '144.cy1.a1', '144.ea1.a1', '144.ea1.b1'], 'contains': ['576.c1.a1', '864.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5178, -1, 5841, -1, 5672, -1, 6554, -1], 'generators': [1634131, 47089], 'label': '1728.46354.288.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '288.ba1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335922
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.u1.a2', '96.v1.a1', '144.u1.a1', '144.cb1.a2', '144.cy1.a2', '144.ea1.a2', '144.ea1.b2'], 'contains': ['576.c1.a1', '864.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5178, -1, 5864, -1, 5672, -1, 6570, -1], 'generators': [1634131, 1197949], 'label': '1728.46354.288.ba1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '288.ba1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335923
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1.a1', '96.x1.a1', '96.y1.a1', '144.v1.a1', '144.cc1.a1', '144.cz1.a1', '144.dt1.a1', '144.dt1.b1', '144.dw1.a1', '144.dw1.b1'], 'contains': ['576.a1.a1', '864.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3901, -1, 8883, -1, 8202, -1, 7634, -1], 'generators': [1675405, 622105], 'label': '1728.46354.288.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '288.bb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335924
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1.a1', '96.z1.a1', '144.w1.a1', '144.cd1.a1', '144.da1.a1', '144.dv1.a1', '144.dv1.b1', '144.dx1.a1', '144.dx1.b1'], 'contains': ['576.b1.a1', '864.h1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3878, -1, 8548, -1, 7477, -1, 8739, -1], 'generators': [1675405, 622537], 'label': '1728.46354.288.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '288.bc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335925
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fm1.a1', '96.x1.a1', '96.z1.a1', '144.x1.a1', '144.du1.a1', '144.du1.b1'], 'contains': ['576.d1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9380, -1, 1244, -1, 1668, -1, 1628, -1], 'generators': [1675405, 1341703], 'label': '1728.46354.288.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '288.bd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335926
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fn1.a1', '96.y1.a1', '96.z1.a1', '144.y1.a1'], 'contains': ['576.f1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9418, -1, 1164, -1, 1874, -1, 1969, -1], 'generators': [1675405, 767155], 'label': '1728.46354.288.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1.a1', 'old_label': '288.be1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335927
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ba1.a1', '144.z1.a1', '144.bz1.a1', '144.ce1.a1', '144.cw1.a1', '144.db1.a1', '144.eb1.a1', '144.eb1.b1'], 'contains': ['576.a1.a1', '864.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3458, -1, 9507, -1, 7537, -1, 7494, -1], 'generators': [793657, 622105], 'label': '1728.46354.288.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '288.bf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335928
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.bc1.a1'], 'contains': ['24.n1.a1', '24.r1.a1', '24.t1.a1', '36.cg1.a1', '36.cj1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4094, -1, 6593, -1, 6499, -1, 6881, -1], 'generators': [1651447, 622105, 622537, 835777, 793169, 887131], 'label': '1728.46354.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264335929
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ba1.a1', '144.ba1.a1', '144.ca1.a1', '144.cf1.a1', '144.cx1.a1', '144.dc1.a1', '144.ec1.a1', '144.ec1.b1'], 'contains': ['576.b1.a1', '864.i1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3627, -1, 9336, -1, 7142, -1, 7843, -1], 'generators': [793657, 622537], 'label': '1728.46354.288.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '288.bg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335930
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ba1.a1', '144.bb1.a1', '144.cb1.a1', '144.cg1.a1', '144.cy1.a2', '144.dd1.a1', '144.ed1.a1', '144.ed1.b1'], 'contains': ['576.c1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4359, -1, 6910, -1, 5764, -1, 6683, -1], 'generators': [793657, 1197949], 'label': '1728.46354.288.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '288.bh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335931
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ba1.a1', '144.bb1.a1', '144.cb1.a2', '144.cg1.a1', '144.cy1.a1', '144.dd1.a2', '144.ed1.a2', '144.ed1.b2'], 'contains': ['576.c1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4359, -1, 6885, -1, 5764, -1, 6735, -1], 'generators': [793657, 47089], 'label': '1728.46354.288.bh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '288.bh1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335932
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '288.bi1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '96.bc1.a1', '96.bd1.a1', '144.bc1.a1', '144.ch1.a1', '144.de1.a1', '144.dy1.a1', '144.dy1.b1', '144.eb1.a1', '144.eb1.b1'], 'contains': ['576.a1.a1', '864.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3612, -1, 8871, -1, 7202, -1, 7307, -1], 'generators': [1633789, 622105], 'label': '1728.46354.288.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '288.bi1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335933
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '288.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '96.be1.a1', '96.bf1.a1', '144.bd1.a1', '144.ci1.a1', '144.df1.a1', '144.dz1.a1', '144.dz1.b1', '144.ec1.a1', '144.ec1.b1'], 'contains': ['576.b1.a1', '864.j1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3663, -1, 8537, -1, 7042, -1, 7760, -1], 'generators': [1633789, 622537], 'label': '1728.46354.288.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '288.bj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335934
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '96.bg1.a1', '96.bh1.a1', '144.be1.a1', '144.cj1.a1', '144.dg1.a1', '144.ea1.a1', '144.ea1.b2', '144.ed1.a2', '144.ed1.b1'], 'contains': ['576.c1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5081, -1, 5853, -1, 5634, -1, 6602, -1], 'generators': [1633789, 47089], 'label': '1728.46354.288.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '288.bk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335935
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '96.bg1.a2', '96.bh1.a2', '144.be1.a1', '144.cj1.a1', '144.dg1.a2', '144.ea1.a2', '144.ea1.b1', '144.ed1.a1', '144.ed1.b2'], 'contains': ['576.c1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5081, -1, 5907, -1, 5634, -1, 6586, -1], 'generators': [1633789, 1197949], 'label': '1728.46354.288.bk1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '288.bk1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335936
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '288.bl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fr1.a1', '96.bc1.a1', '96.be1.a1', '96.bg1.a1', '96.bg1.a2', '144.bf1.a1', '144.ee1.a1', '144.ee1.b1'], 'contains': ['576.d1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9034, -1, 480, -1, 981, -1, 938, -1], 'generators': [1633789, 1341703], 'label': '1728.46354.288.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.co1.a1', 'old_label': '288.bl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335937
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '288.bm1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fs1.a1', '96.bc1.a1', '96.bf1.a1', '96.bh1.a1', '96.bh1.a2', '144.bg1.a1'], 'contains': ['576.e1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9478, -1, 290, -1, 827, -1, 884, -1], 'generators': [1633789, 766291], 'label': '1728.46354.288.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bg1.a1', 'old_label': '288.bm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335938
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '288.bn1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ft1.a1', '96.bd1.a1', '96.be1.a1', '96.bh1.a1', '96.bh1.a2', '144.bh1.a1'], 'contains': ['576.f1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9501, -1, 397, -1, 923, -1, 989, -1], 'generators': [1633789, 767155], 'label': '1728.46354.288.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bh1.a1', 'old_label': '288.bn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335939
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.j1.a1', '6.u1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.q1.a1', '36.ch1.a1', '36.ck1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1851, -1, 7083, -1, 6862, -1, 6846, -1], 'generators': [70957, 622105, 887131, 811801, 622537, 793169], 'label': '1728.46354.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264335940
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fu1.a1', '96.bd1.a1', '96.bf1.a1', '96.bg1.a1', '96.bh1.a2', '144.bi1.a1'], 'contains': ['576.g1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9528, -1, 251, -1, 733, -1, 828, -1], 'generators': [1633789, 1342135], 'label': '1728.46354.288.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bi1.a1', 'old_label': '288.bo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335941
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fu1.a2', '96.bd1.a1', '96.bf1.a1', '96.bg1.a2', '96.bh1.a1', '144.bi1.a1'], 'contains': ['576.g1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9528, -1, 332, -1, 733, -1, 802, -1], 'generators': [1633789, 191707], 'label': '1728.46354.288.bo1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bi1.a1', 'old_label': '288.bo1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335942
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '6.b1.a1', 'complements': ['4.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.d1.a1', '144.e1.a1', '144.dp1.a1', '144.dq1.a1', '144.dr1.a1', '144.ds1.a1', '216.a1.a1', '216.bx1.a1', '216.by1.a1', '216.by1.b1', '216.bz1.a1', '216.ca1.a1', '216.cb1.a1'], 'contains': ['864.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8340, 3967, 2444, 6076, 2853, 4618, 1907, 5435], 'generators': [887131, 70633], 'label': '1728.46354.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.c1.a1', '144.d1.a1', '144.e1.a1', '216.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '6.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264335943
    {'ambient': '1728.46354', 'aut_centralizer_order': 2304, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '144.g1.a1', '144.h1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.i1.a1', '216.j1.a1', '216.k1.a1', '216.l1.a1', '216.m1.a1', '216.n1.a1', '216.o1.a1'], 'contains': ['864.a1.a1', '864.b1.a1', '864.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2782, -1, 7175, -1, 6577, -1, 6770, -1], 'generators': [793169, 887131], 'label': '1728.46354.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335944
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.i1.a1', '144.j1.a1', '144.k1.a1', '216.b1.a1', '216.p1.a1', '216.q1.a1', '216.r1.a1', '216.s1.a1'], 'contains': ['864.a1.a1', '864.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4004, -1, 7309, -1, 7002, -1, 7236, -1], 'generators': [1674451, 793169], 'label': '1728.46354.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335945
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.l1.a1', '144.m1.a1', '144.n1.a1', '144.o1.a1', '216.c1.a1', '216.p1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1', '216.w1.a1', '216.x1.a1'], 'contains': ['864.a1.a1', '864.e1.a1', '864.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1567, -1, 7559, -1, 7223, -1, 7512, -1], 'generators': [46999, 793169], 'label': '1728.46354.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 36, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '432.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335946
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.p1.a1', '144.q1.a1', '216.b1.a1', '216.d1.a1', '216.t1.a1', '216.y1.a1', '216.z1.a1', '216.ba1.a1', '216.bb1.a1'], 'contains': ['864.a1.a1', '864.f1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1551, -1, 8860, -1, 7580, -1, 7690, -1], 'generators': [835273, 793169], 'label': '1728.46354.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335947
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1', '216.e1.a1', '216.q1.a1', '216.u1.a1', '216.y1.a1', '216.bc1.a1'], 'contains': ['864.a1.a1', '864.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3845, -1, 7335, -1, 6980, -1, 7189, -1], 'generators': [1634131, 793169], 'label': '1728.46354.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '432.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335948
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1', '216.f1.a1', '216.p1.a1', '216.t1.a1', '216.bc1.a1', '216.bd1.a1', '216.be1.a1', '216.bf1.a1'], 'contains': ['864.a1.a1', '864.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1793, -1, 7496, -1, 7245, -1, 7530, -1], 'generators': [1675405, 793169], 'label': '1728.46354.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335949
    {'ambient': '1728.46354', 'aut_centralizer_order': 128, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '54.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1.a1', '144.ba1.a1', '144.bb1.a1', '216.e1.a1', '216.g1.a1', '216.r1.a1', '216.v1.a1', '216.z1.a1', '216.ba1.a1', '216.bd1.a1'], 'contains': ['864.a1.a1', '864.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1816, -1, 8372, -1, 7395, -1, 7548, -1], 'generators': [793657, 793169], 'label': '1728.46354.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '432.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335950
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 6, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.p1.a1', '6.r1.a1', '6.w1.a1', '6.y1.a1', '6.ba1.a1', '6.bf1.a1', '9.b1.a1', '9.c1.a1', '12.ck1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5450, -1, 4570, -1, 2396, -1, 3419, -1], 'generators': [46999, 1341703, 622537, 1674451, 793169, 70633, 887131, 835777], 'label': '1728.46354.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264335951
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '24.cw1.a1', '36.cl1.a1', '36.cm1.a1', '36.cn1.a1', '48.h1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7672, -1, 3345, -1, 1737, -1, 2053, -1], 'generators': [1674451, 70633, 887131, 793169, 1341703, 622105], 'label': '1728.46354.12.bl1.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.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264335952
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1.a1', '144.bd1.a1', '144.be1.a1', '144.bf1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1', '216.h1.a1', '216.s1.a1', '216.u1.a1', '216.v1.a1', '216.bb1.a1', '216.be1.a1', '216.bf1.a1'], 'contains': ['864.a1.a1', '864.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2191, -1, 7322, -1, 6958, -1, 6982, -1], 'generators': [1633789, 793169], 'label': '1728.46354.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '432.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335953
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.bl1.a1', '144.bo1.a1', '144.br1.a1', '216.i1.a1', '216.q1.a1', '216.w1.a1', '216.z1.a1', '216.be1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1611, -1, 7142, -1, 7023, -1, 7253, -1], 'generators': [835777], 'label': '1728.46354.432.j1.a1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '432.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335954
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1.a1', '144.bm1.a1', '216.i1.a1', '216.k1.a1', '216.r1.a1', '216.x1.a1', '216.y1.a1', '216.ba1.a1', '216.bf1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1597, -1, 8520, -1, 7518, -1, 7707, -1], 'generators': [1674955], 'label': '1728.46354.432.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '432.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335955
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1.a1', '144.bn1.a1', '144.bp1.a1', '144.bq1.a1', '216.l1.a1', '216.s1.a1', '216.w1.a1', '216.x1.a1', '216.bb1.a1', '216.bc1.a1', '216.bd1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [934, -1, 7349, -1, 7183, -1, 7353, -1], 'generators': [834823], 'label': '1728.46354.432.l1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '432.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335956
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bs1.a1', '144.bt1.a1', '216.b1.a1', '216.bg1.a1', '216.bk1.a1'], 'contains': ['864.b1.a1', '864.d1.a1', '864.f1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3912, -1, 7380, -1, 7497, -1, 7860, -1], 'generators': [1674451, 1633643], 'label': '1728.46354.432.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '432.m1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335957
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bu1.a1', '144.bv1.a1', '144.bw1.a1', '216.c1.a1', '216.bg1.a1', '216.bh1.a1'], 'contains': ['864.b1.a1', '864.e1.a1', '864.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2719, -1, 9249, -1, 7624, -1, 7878, -1], 'generators': [46999, 1633643], 'label': '1728.46354.432.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '432.n1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335958
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bx1.a1', '144.by1.a1', '216.d1.a1', '216.bi1.a1', '216.bk1.a1'], 'contains': ['864.b1.a1', '864.f1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1840, -1, 6963, -1, 7417, -1, 7672, -1], 'generators': [1651771, 1633643], 'label': '1728.46354.432.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '432.o1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335959
    {'ambient': '1728.46354', 'aut_centralizer_order': 128, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '54.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bz1.a1', '144.ca1.a1', '144.cb1.a1', '144.cb1.a2', '216.e1.a1', '216.bh1.a1', '216.bm1.a1'], 'contains': ['864.b1.a1', '864.g1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3987, -1, 7367, -1, 7082, -1, 7211, -1], 'generators': [1634131, 1633643], 'label': '1728.46354.432.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '432.p1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335960
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cc1.a1', '144.cd1.a1', '216.f1.a1', '216.bg1.a1', '216.bj1.a1'], 'contains': ['864.b1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2817, -1, 9210, -1, 8223, -1, 8522, -1], 'generators': [1675405, 1633643], 'label': '1728.46354.432.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '432.q1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335961
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ce1.a1', '144.cf1.a1', '144.cg1.a1', '216.g1.a1', '216.bj1.a1', '216.bm1.a1'], 'contains': ['864.b1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2924, -1, 6950, -1, 7162, -1, 7477, -1], 'generators': [1656811, 1633643], 'label': '1728.46354.432.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.n1.a1', 'old_label': '432.r1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335962
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.s1.a1'], 'contains': ['24.v1.a1', '24.cz1.a1', '36.a1.a1', '36.cn1.a1', '48.j1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7808, -1, 2106, -1, 553, -1, 1197, -1], 'generators': [1674451, 622537, 70633, 793169, 766291, 887131], 'label': '1728.46354.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264335963
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1.a1', '144.ci1.a1', '144.cj1.a1', '216.h1.a1', '216.bh1.a1', '216.bi1.a1'], 'contains': ['864.b1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2166, -1, 8873, -1, 7602, -1, 7793, -1], 'generators': [1633789, 1633643], 'label': '1728.46354.432.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '432.s1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335964
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ck1.a1', '144.cl1.a1', '216.n1.a1', '216.bi1.a1', '216.bj1.a1'], 'contains': ['864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2756, -1, 9133, -1, 8161, -1, 8341, -1], 'generators': [812125], 'label': '1728.46354.432.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1.a1', 'old_label': '432.t1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335965
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '432.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cm1.a1', '144.cn1.a1', '144.co1.a1', '216.a1.a1', '216.bk1.a1', '216.bl1.a1', '216.bl1.b1', '216.bm1.a1', '216.bn1.a1', '216.bo1.a1'], 'contains': ['864.b1.a1', '864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5611, -1, 4333, -1, 4210, -1, 4494, -1], 'generators': [817145, 887131], 'label': '1728.46354.432.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.u1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335966
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '432.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cp1.a1', '144.cq1.a1', '216.b1.a1', '216.bk1.a1', '216.bp1.a1', '216.bp1.b1', '216.bq1.a1', '216.bq1.b1', '216.bx1.a1'], 'contains': ['864.c1.a1', '864.d1.a1', '864.f1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6821, -1, 5018, -1, 5239, -1, 5576, -1], 'generators': [1674451, 887131], 'label': '1728.46354.432.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '432.v1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335967
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1.a1', '144.cs1.a1', '144.ct1.a1', '216.c1.a1', '216.bl1.a1', '216.bp1.a1', '216.br1.a1', '216.bs1.a1', '216.bt1.a1', '216.by1.a1'], 'contains': ['864.c1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6427, -1, 4259, -1, 4245, -1, 4524, -1], 'generators': [46999, 887131], 'label': '1728.46354.432.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.w1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335968
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1.b1', '144.cs1.b1', '144.ct1.b1', '216.c1.a1', '216.bl1.b1', '216.bp1.b1', '216.br1.b1', '216.bs1.b1', '216.bt1.b1', '216.by1.b1'], 'contains': ['864.c1.a1', '864.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6427, -1, 4320, -1, 4245, -1, 4542, -1], 'generators': [793511, 887131], 'label': '1728.46354.432.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.w1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335969
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1.a1', '144.cv1.a1', '216.d1.a1', '216.bk1.a1', '216.br1.a1', '216.br1.b1', '216.bu1.a1', '216.bu1.b1', '216.bx1.a1'], 'contains': ['864.c1.a1', '864.f1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7045, -1, 5207, -1, 4647, -1, 5286, -1], 'generators': [1651771, 887131], 'label': '1728.46354.432.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '432.x1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335970
    {'ambient': '1728.46354', 'aut_centralizer_order': 128, 'aut_label': '432.y1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '54.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1.a1', '144.cx1.a1', '144.cy1.a1', '144.cy1.a2', '216.e1.a1', '216.bm1.a1', '216.bs1.a1', '216.bs1.b1', '216.bv1.a1', '216.bv1.b1', '216.bz1.a1'], 'contains': ['864.c1.a1', '864.g1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5822, -1, 3428, -1, 4138, -1, 3769, -1], 'generators': [1634131, 887131], 'label': '1728.46354.432.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '432.y1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335971
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cz1.a1', '144.da1.a1', '216.f1.a1', '216.bn1.a1', '216.bp1.a1', '216.bp1.b1', '216.bu1.a1', '216.bu1.b1', '216.ca1.a1'], 'contains': ['864.c1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6863, -1, 5129, -1, 5035, -1, 5597, -1], 'generators': [1675405, 887131], 'label': '1728.46354.432.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '432.z1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335972
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.ba1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1.a1', '144.dc1.a1', '144.dd1.a1', '144.dd1.a2', '216.g1.a1', '216.bm1.a1', '216.bt1.a1', '216.bt1.b1', '216.bw1.a1', '216.bw1.b1', '216.bz1.a1'], 'contains': ['864.c1.a1', '864.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5638, -1, 3645, -1, 4048, -1, 3684, -1], 'generators': [1656811, 887131], 'label': '1728.46354.432.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '432.ba1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335973
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.o1.a1', '6.t1.a1', '6.u1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.o1.a1', '24.ck1.a1', '24.ck1.b1', '24.da1.a1', '24.da1.b1', '36.co1.a1', '36.cp1.a1', '36.cq1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5871, -1, 4837, -1, 4070, -1, 4155, -1], 'generators': [46999, 887131, 622105, 793169, 70633, 622537], 'label': '1728.46354.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264335974
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.bb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.de1.a1', '144.df1.a1', '144.dg1.a1', '144.dg1.a2', '216.h1.a1', '216.bo1.a1', '216.bs1.a1', '216.bs1.b1', '216.bw1.a1', '216.bw1.b1', '216.cb1.a1'], 'contains': ['864.c1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5922, -1, 3166, -1, 4016, -1, 3740, -1], 'generators': [1633789, 887131], 'label': '1728.46354.432.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '432.bb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335975
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dh1.a1', '144.dk1.a1', '144.dn1.a1', '216.j1.a1', '216.bl1.b1', '216.bq1.a1', '216.bu1.a1', '216.bv1.a1', '216.bw1.a1', '216.by1.a1'], 'contains': ['864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6799, -1, 4288, -1, 4158, -1, 4465, -1], 'generators': [70957], 'label': '1728.46354.432.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.bc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335976
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dh1.b1', '144.dk1.b1', '144.dn1.b1', '216.j1.a1', '216.bl1.a1', '216.bq1.b1', '216.bu1.b1', '216.bv1.b1', '216.bw1.b1', '216.by1.b1'], 'contains': ['864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6799, -1, 4122, -1, 4158, -1, 4445, -1], 'generators': [817469], 'label': '1728.46354.432.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.bc1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335977
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '432.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.di1.a1', '144.dl1.a1', '216.m1.a1', '216.bn1.a1', '216.bq1.a1', '216.bq1.b1', '216.br1.a1', '216.br1.b1', '216.ca1.a1'], 'contains': ['864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7060, -1, 4869, -1, 4518, -1, 5074, -1], 'generators': [1651447], 'label': '1728.46354.432.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '432.bd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335978
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '432.be1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dj1.a1', '144.dm1.a1', '144.do1.a1', '144.do1.a2', '216.o1.a1', '216.bo1.a1', '216.bt1.a1', '216.bt1.b1', '216.bv1.a1', '216.bv1.b1', '216.cb1.a1'], 'contains': ['864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5777, -1, 3234, -1, 3694, -1, 3630, -1], 'generators': [1656487], 'label': '1728.46354.432.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '432.be1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335979
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dt1.a1', '144.du1.a1', '144.dv1.a1', '216.p1.a1', '216.bg1.a1', '216.bp1.a1'], 'contains': ['864.d1.a1', '864.e1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4945, -1, 7525, -1, 7308, -1, 7583, -1], 'generators': [46999, 1674451], 'label': '1728.46354.432.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.bf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335980
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dt1.b1', '144.du1.b1', '144.dv1.b1', '216.p1.a1', '216.bg1.a1', '216.bp1.b1'], 'contains': ['864.d1.a1', '864.e1.b1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4945, -1, 7512, -1, 7308, -1, 7617, -1], 'generators': [793511, 1674451], 'label': '1728.46354.432.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.bf1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335981
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dw1.a1', '144.dx1.a1', '216.t1.a1', '216.bg1.a1', '216.bp1.a1'], 'contains': ['864.e1.a1', '864.f1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3607, -1, 9236, -1, 8181, -1, 8426, -1], 'generators': [46999, 835273], 'label': '1728.46354.432.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.bg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335982
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dw1.b1', '144.dx1.b1', '216.t1.a1', '216.bg1.a1', '216.bp1.b1'], 'contains': ['864.e1.b1', '864.f1.a1', '864.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3607, -1, 9223, -1, 8181, -1, 8445, -1], 'generators': [793511, 835273], 'label': '1728.46354.432.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.bg1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335983
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dy1.a1', '144.dz1.a1', '144.ea1.a1', '144.ea1.a2', '144.ee1.a1', '216.u1.a1', '216.bh1.a1', '216.bs1.a1'], 'contains': ['864.e1.a1', '864.g1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4052, -1, 7399, -1, 6917, -1, 6929, -1], 'generators': [46999, 1634131], 'label': '1728.46354.432.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '432.bh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335984
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.x1.a1'], 'contains': ['24.w1.a1', '24.db1.a1', '24.db1.b1', '36.b1.a1', '36.cq1.a1', '48.n1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8523, -1, 931, -1, 1123, -1, 588, -1], 'generators': [46999, 70633, 887131, 793169, 47089, 1341703], 'label': '1728.46354.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.bo1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264335985
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dy1.b1', '144.dz1.b1', '144.ea1.b1', '144.ea1.b2', '144.ee1.b1', '216.u1.a1', '216.bh1.a1', '216.bs1.b1'], 'contains': ['864.e1.b1', '864.g1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4052, -1, 7412, -1, 6917, -1, 6964, -1], 'generators': [793511, 1634131], 'label': '1728.46354.432.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '432.bh1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335986
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eb1.a1', '144.ec1.a1', '144.ed1.a1', '144.ed1.a2', '216.v1.a1', '216.bh1.a1', '216.bs1.a1'], 'contains': ['864.e1.a1', '864.i1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2702, -1, 7585, -1, 7286, -1, 7725, -1], 'generators': [46999, 793657], 'label': '1728.46354.432.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '432.bi1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335987
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eb1.b1', '144.ec1.b1', '144.ed1.b1', '144.ed1.b2', '216.v1.a1', '216.bh1.a1', '216.bs1.b1'], 'contains': ['864.e1.b1', '864.i1.a1', '864.j1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2702, -1, 7572, -1, 7286, -1, 7743, -1], 'generators': [793511, 793657], 'label': '1728.46354.432.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '432.bi1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335988
    {'ambient': '1728.46354', 'aut_centralizer_order': 3456, 'aut_label': '576.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.a1.a1', 'complements': ['3.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '288.a1.a1', '288.h1.a1', '288.k1.a1', '288.n1.a1', '288.r1.a1', '288.r1.b1', '288.v1.a1', '288.y1.a1', '288.bb1.a1', '288.bf1.a1', '288.bi1.a1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3776, 5292, 8737, 4806, 7507, 5061, 7419, 4824], 'generators': [622105], 'label': '1728.46354.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['144.c1.a1', '192.a1.a1', '288.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.1028', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335989
    {'ambient': '1728.46354', 'aut_centralizer_order': 3456, 'aut_label': '576.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.e1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.d1.a1', '192.e1.a1', '288.b1.a1', '288.i1.a1', '288.l1.a1', '288.q1.a1', '288.s1.a1', '288.s1.b1', '288.w1.a1', '288.z1.a1', '288.bc1.a1', '288.bg1.a1', '288.bj1.a1'], 'contains': ['1728.a1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3839, 6000, 8327, 4448, 7082, 5858, 7843, 5147], 'generators': [622537], 'label': '1728.46354.576.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.b1.a1', 'normal_contained_in': ['144.d1.a1', '192.a1.a1', '288.b1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.b1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.853', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335990
    {'ambient': '1728.46354', 'aut_centralizer_order': 1728, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.f1.a1', '192.g1.a1', '288.c1.a1', '288.j1.a1', '288.m1.a1', '288.t1.a1', '288.t1.b1', '288.ba1.a1', '288.ba1.a2', '288.bh1.a1', '288.bh1.a2', '288.bk1.a1', '288.bk1.a2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5081, -1, 5904, -1, 5672, -1, 6602, -1], 'generators': [47089], 'label': '1728.46354.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '576.c1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335991
    {'ambient': '1728.46354', 'aut_centralizer_order': 864, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '192.b1.a1', '192.d1.a1', '192.f1.a1', '288.d1.a1', '288.o1.a1', '288.u1.a1', '288.u1.b1', '288.x1.a1', '288.bd1.a1', '288.bl1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9290, -1, 899, -1, 1323, -1, 1166, -1], 'generators': [1341703], 'label': '1728.46354.576.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '576.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335992
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dq1.a1', '192.b1.a1', '192.e1.a1', '192.g1.a1', '288.e1.a1', '288.p1.a1', '288.bm1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9496, -1, 761, -1, 942, -1, 1083, -1], 'generators': [766291], 'label': '1728.46354.576.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '576.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335993
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dr1.a1', '192.c1.a1', '192.d1.a1', '192.g1.a1', '288.f1.a1', '288.be1.a1', '288.bn1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9630, -1, 808, -1, 1271, -1, 1265, -1], 'generators': [767155], 'label': '1728.46354.576.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '576.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335994
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ds1.a1', '192.c1.a1', '192.e1.a1', '192.f1.a1', '192.g1.a1', '288.g1.a1', '288.bo1.a1', '288.bo1.a2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9665, -1, 443, -1, 913, -1, 921, -1], 'generators': [1342135], 'label': '1728.46354.576.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.f1.a1', 'old_label': '576.g1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264335995
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.m1.a1', '6.v1.a1', '6.z1.a1'], 'contains': ['24.b1.a1', '24.dc1.a1', '36.cr1.a1', '36.cs1.a1', '48.p1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7228, -1, 3298, -1, 1671, -1, 1738, -1], 'generators': [1634131, 622105, 70633, 793169, 1341703, 887131], 'label': '1728.46354.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264335996
    {'ambient': '1728.46354', 'aut_centralizer_order': 6912, 'aut_label': '864.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '288.b1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.f1.a1', '288.g1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '432.e1.a1', '432.f1.a1', '432.g1.a1', '432.h1.a1', '432.i1.a1', '432.j1.a1', '432.k1.a1', '432.l1.a1'], 'contains': ['1728.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2191, 5654, 7345, 4109, 7002, 5409, 7253, 4459], 'generators': [793169], 'label': '1728.46354.864.a1.a1', 'mobius_quo': -1, 'mobius_sub': -864, 'normal_closure': '864.a1.a1', 'normal_contained_in': ['216.a1.a1', '288.a1.a1', '288.b1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '1.1', 'quotient_action_kernel': '864.4673', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335997
    {'ambient': '1728.46354', 'aut_centralizer_order': 2304, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.h1.a1', '288.i1.a1', '288.j1.a1', '432.b1.a1', '432.m1.a1', '432.n1.a1', '432.o1.a1', '432.p1.a1', '432.q1.a1', '432.r1.a1', '432.s1.a1', '432.t1.a1', '432.u1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2804, -1, 7561, -1, 7447, -1, 7673, -1], 'generators': [1633643], 'label': '1728.46354.864.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '864.b1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335998
    {'ambient': '1728.46354', 'aut_centralizer_order': 2304, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1.a1', '288.l1.a1', '288.m1.a1', '432.a1.a1', '432.b1.a1', '432.u1.a1', '432.v1.a1', '432.w1.a1', '432.w1.b1', '432.x1.a1', '432.y1.a1', '432.z1.a1', '432.ba1.a1', '432.bb1.a1', '432.bc1.a1', '432.bc1.b1', '432.bd1.a1', '432.be1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6806, -1, 4311, -1, 4245, -1, 4524, -1], 'generators': [887131], 'label': '1728.46354.864.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '864.c1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264335999
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.n1.a1', '288.o1.a1', '288.p1.a1', '288.q1.a1', '432.c1.a1', '432.m1.a1', '432.v1.a1', '432.bf1.a1', '432.bf1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4972, -1, 7318, -1, 6947, -1, 7282, -1], 'generators': [1674451], 'label': '1728.46354.864.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '864.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336000
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.r1.a1', '288.s1.a1', '288.t1.a1', '288.u1.a1', '432.d1.a1', '432.n1.a1', '432.w1.a1', '432.bf1.a1', '432.bg1.a1', '432.bh1.a1', '432.bi1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3790, -1, 7548, -1, 7224, -1, 7530, -1], 'generators': [46999], 'label': '1728.46354.864.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '864.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336001
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.r1.b1', '288.s1.b1', '288.t1.b1', '288.u1.b1', '432.d1.a1', '432.n1.a1', '432.w1.b1', '432.bf1.b1', '432.bg1.b1', '432.bh1.b1', '432.bi1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3790, -1, 7534, -1, 7224, -1, 7582, -1], 'generators': [793511], 'label': '1728.46354.864.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '864.e1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336002
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.v1.a1', '288.w1.a1', '432.e1.a1', '432.m1.a1', '432.o1.a1', '432.v1.a1', '432.x1.a1', '432.bg1.a1', '432.bg1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3692, -1, 7409, -1, 7417, -1, 7758, -1], 'generators': [835273], 'label': '1728.46354.864.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '864.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336003
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.x1.a1', '288.y1.a1', '288.z1.a1', '288.ba1.a1', '288.ba1.a2', '432.f1.a1', '432.p1.a1', '432.y1.a1', '432.bh1.a1', '432.bh1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4067, -1, 7333, -1, 6922, -1, 6964, -1], 'generators': [1634131], 'label': '1728.46354.864.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '864.g1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336004
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1.a1', '288.bc1.a1', '288.bd1.a1', '288.be1.a1', '432.g1.a1', '432.q1.a1', '432.z1.a1', '432.bf1.a1', '432.bf1.b1', '432.bg1.a1', '432.bg1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4023, -1, 7513, -1, 7276, -1, 7607, -1], 'generators': [1675405], 'label': '1728.46354.864.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '864.h1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336005
    {'ambient': '1728.46354', 'aut_centralizer_order': 128, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '54.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bf1.a1', '288.bg1.a1', '288.bh1.a1', '288.bh1.a2', '432.h1.a1', '432.p1.a1', '432.r1.a1', '432.y1.a1', '432.ba1.a1', '432.bi1.a1', '432.bi1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3651, -1, 7371, -1, 7112, -1, 7325, -1], 'generators': [793657], 'label': '1728.46354.864.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '864.i1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336006
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.p1.a1', '6.w1.a1', '6.ba1.a1'], 'contains': ['24.c1.a1', '24.dd1.a1', '36.cr1.a1', '36.ct1.a1', '48.q1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7130, -1, 3253, -1, 1356, -1, 2006, -1], 'generators': [1634131, 622537, 70633, 793169, 1341703, 887131], 'label': '1728.46354.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.bq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336007
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bi1.a1', '288.bj1.a1', '288.bk1.a1', '288.bk1.a2', '288.bl1.a1', '288.bm1.a1', '288.bn1.a1', '288.bo1.a1', '288.bo1.a2', '432.i1.a1', '432.s1.a1', '432.bb1.a1', '432.bh1.a1', '432.bh1.b1', '432.bi1.a1', '432.bi1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4052, -1, 7110, -1, 6903, -1, 6929, -1], 'generators': [1633789], 'label': '1728.46354.864.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.h1.a1', 'old_label': '864.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336008
    {'ambient': '1728.46354', 'aut_centralizer_order': None, 'aut_label': '1728.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': ['576.a1.a1', '576.b1.a1', '576.c1.a1', '576.d1.a1', '576.e1.a1', '576.f1.a1', '576.g1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1', '864.d1.a1', '864.e1.a1', '864.e1.b1', '864.f1.a1', '864.g1.a1', '864.h1.a1', '864.i1.a1', '864.j1.a1'], 'contains': [], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4052, 5508, 7340, 4681, 6947, 5235, 7261, 4985], 'generators': [], 'label': '1728.46354.1728.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1728.a1.a1', 'normal_contained_in': ['432.a1.a1', '576.a1.a1', '576.b1.a1', '864.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336009
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.x1.a1'], 'contains': ['24.w1.a1', '24.de1.a1', '24.de1.a2', '36.cr1.a1', '36.cu1.a1', '48.r1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7858, -1, 1112, -1, 879, -1, 626, -1], 'generators': [1634131, 47089, 70633, 793169, 1341703, 887131], 'label': '1728.46354.12.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.br1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336010
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.o1.a1', '6.bb1.a1', '6.bc1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '24.r1.a1', '24.cm1.a1', '24.dg1.a1', '36.cv1.a1', '36.cw1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5210, -1, 5449, -1, 4778, -1, 5300, -1], 'generators': [1675405, 622537, 887131, 793169, 70633, 622105], 'label': '1728.46354.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336011
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.l1.a1', '6.z1.a1', '6.bd1.a1'], 'contains': ['24.b1.a1', '24.dh1.a1', '36.cv1.a1', '36.cx1.a1', '48.t1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7937, -1, 3514, -1, 2407, -1, 3419, -1], 'generators': [1675405, 70633, 887131, 793169, 622105, 1341703], 'label': '1728.46354.12.bt1.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.bt1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336012
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.be1.a1'], 'contains': ['24.u1.a1', '24.di1.a1', '36.cv1.a1', '36.cy1.a1', '48.u1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8719, -1, 2344, -1, 2078, -1, 5112, -1], 'generators': [1675405, 70633, 887131, 793169, 622105, 767155], 'label': '1728.46354.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1.a1', 'old_label': '12.bu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336013
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.a1.a1', 'complements': ['432.bh1.a1', '432.bi1.a1', '432.bh1.b1', '432.bi1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '12.a1.a1', '12.b1.a1', '12.bl1.a1', '12.bm1.a1', '16.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7602, 8006, 3144, 2273, 1704, 8531, 2083, 4378], 'generators': [1674451, 70633, 887131, 793169, 622537, 1341703, 622105], 'label': '1728.46354.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336014
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.q1.a1', '6.t1.a1', '6.bc1.a1'], 'contains': ['24.a1.a1', '24.m1.a1', '24.t1.a1', '24.cn1.a1', '24.dk1.a1', '36.cz1.a1', '36.da1.a1', '36.db1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5495, -1, 5194, -1, 3741, -1, 4063, -1], 'generators': [1633789, 622105, 622537, 793169, 70633, 887131], 'label': '1728.46354.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336015
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.n1.a1', '6.v1.a1', '6.bd1.a1'], 'contains': ['24.b1.a1', '24.dl1.a1', '36.cz1.a1', '36.dc1.a1', '36.dd1.a1', '48.y1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7527, -1, 3065, -1, 1208, -1, 1349, -1], 'generators': [1633789, 70633, 887131, 793169, 1341703, 622105], 'label': '1728.46354.12.bw1.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.bw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336016
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.be1.a1'], 'contains': ['24.u1.a1', '24.dm1.a1', '36.cz1.a1', '36.de1.a1', '36.df1.a1', '48.z1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9157, -1, 2210, -1, 999, -1, 1897, -1], 'generators': [1633789, 70633, 887131, 793169, 767155, 622105], 'label': '1728.46354.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1.a1', 'old_label': '12.bx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336017
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.r1.a1', '6.w1.a1', '6.bf1.a1'], 'contains': ['24.c1.a1', '24.dn1.a1', '36.da1.a1', '36.dc1.a1', '36.de1.a1', '48.ba1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7022, -1, 2495, -1, 1163, -1, 1964, -1], 'generators': [1633789, 70633, 887131, 793169, 1341703, 622537], 'label': '1728.46354.12.by1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.by1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336018
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.s1.a1'], 'contains': ['24.v1.a1', '24.do1.a1', '36.da1.a1', '36.dd1.a1', '36.df1.a1', '48.bb1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8274, -1, 1228, -1, 214, -1, 806, -1], 'generators': [1633789, 70633, 887131, 793169, 766291, 622537], 'label': '1728.46354.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.bz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336019
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.x1.a1'], 'contains': ['24.w1.a1', '24.dp1.a1', '24.dp1.a2', '36.db1.a1', '36.dc1.a1', '36.df1.a1', '48.bc1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8749, -1, 907, -1, 503, -1, 554, -1], 'generators': [1633789, 70633, 887131, 793169, 1341703, 47089], 'label': '1728.46354.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.ca1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336020
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.189', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['24.x1.a1', '24.dq1.a1', '24.dq1.a2', '36.db1.a1', '36.dd1.a1', '36.de1.a1', '36.df1.a1', '48.bd1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8898, -1, 1181, -1, 373, -1, 709, -1], 'generators': [1633789, 70633, 887131, 793169, 766291, 47089], 'label': '1728.46354.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cb1.a1', 'old_label': '12.cb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 264336021
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.q1.a1', '6.u1.a1', '6.bb1.a1'], 'contains': ['24.a1.a1', '24.q1.a1', '24.s1.a1', '36.dg1.a1', '36.di1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4806, -1, 6717, -1, 5523, -1, 6120, -1], 'generators': [834823, 622105, 887131, 70633, 622537, 793169], 'label': '1728.46354.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336022
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.be1.a1'], 'contains': ['24.u1.a1', '36.c1.a1', '36.dm1.a1', '48.bi1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6831, -1, 3183, -1, 2367, -1, 5166, -1], 'generators': [835777, 622105, 70633, 767155, 793169, 887131], 'label': '1728.46354.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '12.cd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336023
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.p1.a1', '6.y1.a1', '6.bf1.a1'], 'contains': ['24.c1.a1', '36.dh1.a1', '36.dj1.a1', '36.dm1.a1', '48.bj1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4717, -1, 3925, -1, 2457, -1, 3780, -1], 'generators': [835777, 70633, 887131, 1341703, 622537, 793169], 'label': '1728.46354.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.ce1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336024
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1', '12.d1.a1', '12.bn1.a1', '12.bo1.a1', '16.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7722, 792, 2413, 8739, 1760, 1264, 1615, 8889], 'generators': [46999, 887131, 1341703, 793169, 70633, 622537, 622105], 'label': '1728.46354.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '864.4673', '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': '96.226'}
  • id: 264336025
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.r1.a1', '6.y1.a1', '6.ba1.a1'], 'contains': ['24.c1.a1', '36.di1.a1', '36.dk1.a1', '48.bk1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5725, -1, 5527, -1, 2780, -1, 2664, -1], 'generators': [834823, 70633, 887131, 622537, 793169, 1341703], 'label': '1728.46354.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.cf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336026
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.s1.a1'], 'contains': ['24.v1.a1', '36.di1.a1', '36.dl1.a1', '48.bl1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7280, -1, 4065, -1, 2027, -1, 1619, -1], 'generators': [834823, 70633, 887131, 622537, 793169, 766291], 'label': '1728.46354.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '12.cg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336027
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.h1.a1'], 'contains': ['24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bn1.a1', '24.bq1.a1', '24.bw1.a1', '24.cc1.a1', '36.dn1.a1', '36.dp1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5938, -1, 5273, -1, 2633, -1, 3476, -1], 'generators': [46999, 622105, 1341703, 1674451, 835777, 793169], 'label': '1728.46354.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '12.ch1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336028
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.d1.a1'], 'contains': ['24.d1.a1', '24.bb1.a1', '24.bf1.a1', '24.bj1.a1', '24.bl1.a1', '24.by1.a1', '24.ca1.a1', '36.dn1.a1', '36.dq1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3628, -1, 7469, -1, 8677, -1, 8702, -1], 'generators': [46999, 622105, 622537, 1674451, 835777, 793169], 'label': '1728.46354.12.ci1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.ci1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336029
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.bb1.a1', '24.be1.a1', '24.bf1.a1', '24.bk1.a1', '24.bm1.a1', '24.bz1.a1', '24.cb1.a1', '36.do1.a1', '36.dr1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1327, -1, 9116, -1, 9218, -1, 9042, -1], 'generators': [46999, 622105, 622537, 1674451, 1674955, 793169], 'label': '1728.46354.12.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336030
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.ck1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.h1.a1'], 'contains': ['24.bc1.a1', '24.bd1.a1', '24.bg1.a1', '24.bo1.a1', '24.br1.a1', '24.bx1.a1', '24.ce1.a1', '36.dp1.a1', '36.dq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5611, -1, 5247, -1, 2501, -1, 3521, -1], 'generators': [46999, 622537, 1341703, 1674451, 835777, 793169], 'label': '1728.46354.12.ck1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '12.ck1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336031
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.bi1.a1', '24.bj1.a1', '24.bm1.a1', '24.bs1.a1', '24.bv1.a1', '24.by1.a1', '24.cb1.a1', '36.ds1.a1', '36.du1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1044, -1, 9157, -1, 9106, -1, 8923, -1], 'generators': [46999, 622105, 622537, 835273, 1674955, 793169], 'label': '1728.46354.12.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336032
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.bi1.a1', '24.bk1.a1', '24.bl1.a1', '24.bt1.a1', '24.bv1.a1', '24.bz1.a1', '24.ca1.a1', '36.dt1.a1', '36.dv1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1007, -1, 9004, -1, 9157, -1, 8965, -1], 'generators': [46999, 622105, 622537, 835273, 835777, 793169], 'label': '1728.46354.12.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336033
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1'], 'contains': ['24.cj1.a1', '24.ck1.a1', '24.cm1.a1', '24.co1.a1', '24.cp1.b1', '24.cq1.a1', '24.ct1.b1', '36.dw1.a1', '36.dx1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6121, -1, 4995, -1, 4538, -1, 4792, -1], 'generators': [46999, 622537, 887131, 1674451, 817145, 622105], 'label': '1728.46354.12.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '12.cn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336034
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1'], 'contains': ['24.cj1.a1', '24.ck1.b1', '24.cm1.a1', '24.co1.b1', '24.cp1.a1', '24.cq1.b1', '24.ct1.a1', '36.dw1.b1', '36.dx1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6121, -1, 4938, -1, 4538, -1, 5073, -1], 'generators': [70957, 622537, 887131, 1674451, 817145, 622105], 'label': '1728.46354.12.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '12.cn1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336035
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47874', 'aut_weyl_index': 4, 'centralizer': '864.a1.a1', 'complements': ['432.bf1.a1', '432.bg1.a1', '432.bf1.b1', '432.bg1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '12.e1.a1', '12.bp1.a1', '12.bq1.a1', '12.br1.a1', '16.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7334, 6584, 3247, 5523, 1486, 7445, 1812, 2525], 'generators': [1634131, 622537, 70633, 793169, 622105, 1341703, 887131], 'label': '1728.46354.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '864.4673', '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': '864.4673'}
  • id: 264336036
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1'], 'contains': ['24.ck1.a1', '24.cl1.a1', '24.cn1.a1', '24.cr1.a1', '24.cs1.a1', '24.cu1.b1', '24.cv1.b1', '36.dy1.a1', '36.dz1.a1', '36.ea1.a1', '36.ea1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5825, -1, 4098, -1, 3789, -1, 3712, -1], 'generators': [46999, 622105, 622537, 1634131, 817145, 887131], 'label': '1728.46354.12.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.co1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.co1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336037
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1'], 'contains': ['24.ck1.b1', '24.cl1.a1', '24.cn1.a1', '24.cr1.b1', '24.cs1.b1', '24.cu1.a1', '24.cv1.a1', '36.dy1.b1', '36.dz1.b1', '36.ea1.b1', '36.ea1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5825, -1, 4125, -1, 3789, -1, 3638, -1], 'generators': [70957, 622105, 622537, 1634131, 817145, 887131], 'label': '1728.46354.12.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.co1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.co1.b1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336038
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.l1.a1'], 'contains': ['24.e1.a1', '24.cw1.a1', '24.dh1.a1', '36.eb1.a1', '36.ec1.a1', '48.cj1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9187, -1, 2152, -1, 1449, -1, 1461, -1], 'generators': [46999, 70633, 887131, 1674451, 622105, 1341703], 'label': '1728.46354.12.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '12.cp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336039
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.l1.a1'], 'contains': ['24.e1.b1', '24.cw1.a1', '24.dh1.a1', '36.eb1.b1', '36.ec1.b1', '48.cj1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9187, -1, 2180, -1, 1449, -1, 1522, -1], 'generators': [793511, 70633, 887131, 1674451, 622105, 1341703], 'label': '1728.46354.12.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '12.cp1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336040
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.o1.a1'], 'contains': ['24.co1.a1', '24.cp1.a1', '24.cq1.a1', '24.ct1.a1', '24.cx1.a1', '24.da1.a1', '24.dg1.a1', '36.eb1.a1', '36.ed1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7737, -1, 2857, -1, 3664, -1, 3219, -1], 'generators': [46999, 622537, 887131, 1674451, 70633, 622105], 'label': '1728.46354.12.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '12.cq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336041
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.o1.a1'], 'contains': ['24.co1.b1', '24.cp1.b1', '24.cq1.b1', '24.ct1.b1', '24.cx1.a1', '24.da1.b1', '24.dg1.a1', '36.eb1.b1', '36.ed1.b1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7737, -1, 2915, -1, 3664, -1, 3267, -1], 'generators': [793511, 622537, 887131, 1674451, 70633, 622105], 'label': '1728.46354.12.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '12.cq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336042
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.a1.a1'], 'contains': ['24.f1.a1', '24.cy1.a1', '24.dj1.a1', '36.ec1.a1', '36.ed1.a1', '48.cl1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8677, -1, 1283, -1, 1402, -1, 1653, -1], 'generators': [46999, 70633, 887131, 1674451, 1341703, 622537], 'label': '1728.46354.12.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336043
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.a1.a1'], 'contains': ['24.f1.b1', '24.cy1.a1', '24.dj1.a1', '36.ec1.b1', '36.ed1.b1', '48.cl1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8677, -1, 1481, -1, 1402, -1, 1683, -1], 'generators': [793511, 70633, 887131, 1674451, 1341703, 622537], 'label': '1728.46354.12.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cr1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336044
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.t1.a1'], 'contains': ['24.cr1.a1', '24.cs1.a1', '24.cu1.a1', '24.cv1.a1', '24.da1.a1', '24.df1.a1', '24.dk1.a1', '36.ee1.a1', '36.ef1.a1', '36.eg1.a1', '36.eg1.a2'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7634, -1, 2379, -1, 3156, -1, 2761, -1], 'generators': [46999, 622105, 622537, 1634131, 70633, 887131], 'label': '1728.46354.12.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.cs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336045
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.t1.a1'], 'contains': ['24.cr1.b1', '24.cs1.b1', '24.cu1.b1', '24.cv1.b1', '24.da1.b1', '24.df1.a1', '24.dk1.a1', '36.ee1.b1', '36.ef1.b1', '36.eg1.b1', '36.eg1.b2'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7634, -1, 2313, -1, 3156, -1, 2798, -1], 'generators': [793511, 622105, 622537, 1634131, 70633, 887131], 'label': '1728.46354.12.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '12.cs1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cs1.b1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336046
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.a1.a1', 'complements': ['432.bh1.a1', '432.bi1.a1', '432.bh1.b1', '432.bi1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '12.f1.a1', '12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '16.e1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7646, 5487, 3175, 4540, 2174, 5452, 3706, 6353], 'generators': [1675405, 887131, 622537, 793169, 70633, 622105, 1341703], 'label': '1728.46354.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336047
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.v1.a1'], 'contains': ['24.e1.a1', '24.dc1.a1', '24.dl1.a1', '36.ee1.a1', '36.eh1.a1', '48.cp1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8644, -1, 1145, -1, 796, -1, 743, -1], 'generators': [46999, 70633, 887131, 1634131, 1341703, 622105], 'label': '1728.46354.12.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '12.ct1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336048
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.v1.a1'], 'contains': ['24.e1.b1', '24.dc1.a1', '24.dl1.a1', '36.ee1.b1', '36.eh1.b1', '48.cp1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8644, -1, 1050, -1, 796, -1, 773, -1], 'generators': [793511, 70633, 887131, 1634131, 1341703, 622105], 'label': '1728.46354.12.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '12.ct1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336049
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.w1.a1'], 'contains': ['24.f1.a1', '24.dd1.a1', '24.dn1.a1', '36.ef1.a1', '36.eh1.a1', '48.cq1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8575, -1, 953, -1, 716, -1, 840, -1], 'generators': [46999, 70633, 887131, 1634131, 1341703, 622537], 'label': '1728.46354.12.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.cu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336050
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.w1.a1'], 'contains': ['24.f1.b1', '24.dd1.a1', '24.dn1.a1', '36.ef1.b1', '36.eh1.b1', '48.cq1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8575, -1, 511, -1, 716, -1, 996, -1], 'generators': [793511, 70633, 887131, 1634131, 1341703, 622537], 'label': '1728.46354.12.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.cu1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336051
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.x1.a1'], 'contains': ['24.db1.a1', '24.de1.a1', '24.dp1.a1', '36.eg1.a1', '36.eh1.a1', '48.cr1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9229, -1, 270, -1, 628, -1, 268, -1], 'generators': [46999, 70633, 887131, 1634131, 1341703, 47089], 'label': '1728.46354.12.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.cv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336052
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.x1.a1'], 'contains': ['24.db1.a1', '24.de1.a2', '24.dp1.a2', '36.eg1.a2', '36.eh1.a1', '48.cr1.a2'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9229, -1, 237, -1, 628, -1, 325, -1], 'generators': [46999, 70633, 887131, 1634131, 1341703, 1197949], 'label': '1728.46354.12.cv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.cv1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cv1.a2', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336053
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.x1.a1'], 'contains': ['24.db1.b1', '24.de1.a1', '24.dp1.a2', '36.eg1.b1', '36.eh1.b1', '48.cr1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9229, -1, 214, -1, 628, -1, 378, -1], 'generators': [793511, 70633, 887131, 1634131, 1341703, 47089], 'label': '1728.46354.12.cv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.cv1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cv1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336054
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '12.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.x1.a1'], 'contains': ['24.db1.b1', '24.de1.a2', '24.dp1.a1', '36.eg1.b2', '36.eh1.b1', '48.cr1.b2'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9229, -1, 179, -1, 628, -1, 463, -1], 'generators': [793511, 70633, 887131, 1634131, 1341703, 1197949], 'label': '1728.46354.12.cv1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '12.cv1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cv1.b2', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336055
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['108.bj1.a1', '108.bm1.a1', '108.bk1.a1', '108.bl1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.f1.a1', '48.cf1.a1', '48.cg1.a1', '48.ch1.a1', '48.ci1.a1', '64.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9690, 3459, 544, 7136, 444, 4077, 754, 6595], 'generators': [1341703, 70633, 622537, 622105, 887131], 'label': '1728.46354.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['48.d1.a1', '48.e1.a1', '48.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336056
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '48.a1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7624, -1, 3237, -1, 1795, -1, 2089, -1], 'generators': [1674451, 622537, 793169, 1341703, 622105], 'label': '1728.46354.16.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336072
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '36.h1.a1', '36.by1.a1', '36.cb1.a1', '36.cd1.a1', '36.ch1.a1', '54.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1795, -1, 6716, -1, 6741, -1, 6452, -1], 'generators': [70957, 622105, 887131, 1674451, 811801, 793169], 'label': '1728.46354.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336057
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47874', 'aut_weyl_index': 4, 'centralizer': '864.a1.a1', 'complements': ['432.bf1.a1', '432.bg1.a1', '432.bf1.b1', '432.bg1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '12.bv1.a1', '12.bw1.a1', '12.bx1.a1', '12.by1.a1', '12.bz1.a1', '12.ca1.a1', '12.cb1.a1', '16.f1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7681, 3226, 2445, 6560, 1069, 3435, 1499, 3488], 'generators': [1633789, 887131, 622105, 793169, 70633, 1341703, 622537], 'label': '1728.46354.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 264336058
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.c1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8142, -1, 2453, -1, 1903, -1, 1815, -1], 'generators': [46999, 1341703, 793169, 622537, 622105], 'label': '1728.46354.16.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336059
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.b1.a1', '48.p1.a1', '48.q1.a1', '48.r1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7217, -1, 3358, -1, 1609, -1, 1866, -1], 'generators': [1634131, 622105, 793169, 1341703, 622537], 'label': '1728.46354.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336060
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.c1.a1', '8.h1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.s1.a1', '48.t1.a1', '48.u1.a1', '48.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8179, -1, 3115, -1, 2380, -1, 4536, -1], 'generators': [1675405, 622537, 793169, 622105, 1341703], 'label': '1728.46354.16.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336061
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.759', 'aut_weyl_index': 16, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.e1.a1', '8.f1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1', '48.ba1.a1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7716, -1, 2967, -1, 1195, -1, 1672, -1], 'generators': [1633789, 622105, 793169, 1341703, 622537], 'label': '1728.46354.16.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336062
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.d1.a1', '8.g1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '48.bg1.a1', '48.bi1.a1', '48.bj1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4777, -1, 3983, -1, 2593, -1, 3935, -1], 'generators': [835777, 622105, 1341703, 622537, 793169], 'label': '1728.46354.16.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336063
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.e1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.bf1.a1', '48.bh1.a1', '48.bk1.a1', '48.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6718, -1, 5736, -1, 2860, -1, 2607, -1], 'generators': [834823, 622105, 622537, 793169, 1341703], 'label': '1728.46354.16.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336064
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '8.c1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.e1.a1', '48.cj1.a1', '48.ck1.a1', '48.cl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9450, -1, 1421, -1, 1423, -1, 1731, -1], 'generators': [46999, 622537, 1674451, 622105, 1341703], 'label': '1728.46354.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.i1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336065
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '8.c1.a1'], 'contains': ['32.b1.a1', '32.c1.b1', '32.e1.a1', '48.cj1.b1', '48.ck1.b1', '48.cl1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9450, -1, 1476, -1, 1423, -1, 1766, -1], 'generators': [793511, 622537, 1674451, 622105, 1341703], 'label': '1728.46354.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.i1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336066
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.162', 'aut_weyl_index': 32, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '8.f1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.f1.a1', '48.cn1.a1', '48.cp1.a1', '48.cq1.a1', '48.cr1.a1', '48.cr1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8973, -1, 791, -1, 770, -1, 1097, -1], 'generators': [46999, 622105, 1634131, 1341703, 622537], 'label': '1728.46354.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '16.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 264336067
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.162', 'aut_weyl_index': 32, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '8.f1.a1'], 'contains': ['32.c1.b1', '32.d1.a1', '32.f1.a1', '48.cn1.b1', '48.cp1.b1', '48.cq1.b1', '48.cr1.b1', '48.cr1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8973, -1, 678, -1, 770, -1, 1134, -1], 'generators': [793511, 622105, 1634131, 1341703, 622537], 'label': '1728.46354.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '16.j1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 264336068
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.b1.a1', 'complements': ['432.bf1.a1', '432.bg1.a1', '432.bf1.b1', '432.bg1.b1', '432.bh1.a1', '432.bi1.a1', '432.bh1.b1', '432.bi1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.g1.a1', '12.h1.a1', '12.cd1.a1', '12.ce1.a1', '16.g1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4777, 4383, 3963, 3552, 2480, 4468, 3766, 1441], 'generators': [835777, 70633, 887131, 1341703, 622105, 622537, 793169], 'label': '1728.46354.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.g1.a1', '12.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336069
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.g1.a1', '36.r1.a1', '36.x1.a1', '36.bl1.a1', '36.bt1.a1', '36.dn1.a1', '36.do1.a1', '36.ds1.a1', '36.dt1.a1', '54.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1584, -1, 7715, -1, 8506, -1, 7464, -1], 'generators': [46999, 622105, 793169, 1674451, 835777, 887131], 'label': '1728.46354.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336070
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.f1.a1', '36.i1.a1', '36.u1.a1', '36.y1.a1', '36.bs1.a1', '36.bu1.a1', '54.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3307, -1, 7864, -1, 7164, -1, 6722, -1], 'generators': [46999, 622105, 887131, 1674451, 811801, 793169], 'label': '1728.46354.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336071
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.h1.a1', '36.i1.a1', '36.bn1.a1', '36.bo1.a1', '36.cf1.a1', '36.cg1.a1', '54.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3868, -1, 6879, -1, 6537, -1, 6414, -1], 'generators': [70957, 622105, 887131, 1674451, 835777, 793169], 'label': '1728.46354.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336073
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.k1.a1', '36.m1.a1', '36.s1.a1', '36.z1.a1', '36.bm1.a1', '36.bw1.a1', '36.dq1.a1', '36.dr1.a1', '36.du1.a1', '36.dv1.a1', '54.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2178, -1, 7348, -1, 7400, -1, 8367, -1], 'generators': [46999, 622537, 793169, 1674451, 835777, 887131], 'label': '1728.46354.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336074
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.l1.a1', '36.o1.a1', '36.v1.a1', '36.ba1.a1', '36.bv1.a1', '36.bx1.a1', '54.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3416, -1, 7689, -1, 6414, -1, 7247, -1], 'generators': [46999, 622537, 887131, 1674451, 811801, 793169], 'label': '1728.46354.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336075
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.c1.a1'], 'contains': ['36.k1.a1', '36.n1.a1', '36.o1.a1', '36.bp1.a1', '36.bq1.a1', '36.ci1.a1', '36.cj1.a1', '54.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4241, -1, 6687, -1, 5758, -1, 6753, -1], 'generators': [70957, 622537, 887131, 1674451, 835777, 793169], 'label': '1728.46354.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336076
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.c1.a1'], 'contains': ['36.l1.a1', '36.m1.a1', '36.n1.a1', '36.bz1.a1', '36.cc1.a1', '36.ce1.a1', '36.ck1.a1', '54.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2525, -1, 6492, -1, 5908, -1, 6784, -1], 'generators': [70957, 622537, 887131, 1674451, 811801, 793169], 'label': '1728.46354.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336077
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.r1.a1', '36.y1.a1', '36.bb1.a1', '36.be1.a1', '36.bo1.a1', '36.cd1.a1', '54.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2605, -1, 7888, -1, 6940, -1, 6657, -1], 'generators': [46999, 622105, 887131, 1651771, 811801, 793169], 'label': '1728.46354.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336078
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.u1.a1', '36.x1.a1', '36.bd1.a1', '36.bf1.a1', '36.cb1.a1', '36.cg1.a1', '54.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1671, -1, 6390, -1, 6696, -1, 6510, -1], 'generators': [46999, 622105, 887131, 1651771, 835777, 793169], 'label': '1728.46354.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336079
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.b1.a1', 'complements': ['432.bf1.a1', '432.bg1.a1', '432.bf1.b1', '432.bg1.b1', '432.bh1.a1', '432.bi1.a1', '432.bh1.b1', '432.bi1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '12.i1.a1', '12.cc1.a1', '12.cf1.a1', '12.cg1.a1', '16.h1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6733, 2041, 5621, 7621, 2758, 2379, 2607, 5413], 'generators': [834823, 887131, 622105, 622537, 70633, 793169, 1341703], 'label': '1728.46354.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336080
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '36.s1.a1', '36.ba1.a1', '36.bg1.a1', '36.bj1.a1', '36.bq1.a1', '36.ce1.a1', '54.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3120, -1, 7826, -1, 6336, -1, 7043, -1], 'generators': [46999, 622537, 887131, 1651771, 811801, 793169], 'label': '1728.46354.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336081
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '36.v1.a1', '36.z1.a1', '36.bi1.a1', '36.bk1.a1', '36.cc1.a1', '36.cj1.a1', '54.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1911, -1, 6209, -1, 5868, -1, 6915, -1], 'generators': [46999, 622537, 887131, 1651771, 835777, 793169], 'label': '1728.46354.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336082
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.a1.a1'], 'contains': ['36.bb1.a1', '36.bc1.a1', '36.bf1.a1', '36.bl1.a1', '36.bn1.a1', '36.bu1.a1', '36.ch1.a1', '54.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2205, -1, 7297, -1, 6824, -1, 6483, -1], 'generators': [70957, 622105, 887131, 1651771, 811801, 793169], 'label': '1728.46354.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336083
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '9.a1.a1'], 'contains': ['36.bc1.a1', '36.bd1.a1', '36.be1.a1', '36.bs1.a1', '36.bt1.a1', '36.by1.a1', '36.cf1.a1', '54.h1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1830, -1, 7318, -1, 7125, -1, 6689, -1], 'generators': [70957, 622105, 887131, 1651771, 835777, 793169], 'label': '1728.46354.18.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336084
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.c1.a1'], 'contains': ['36.bg1.a1', '36.bh1.a1', '36.bk1.a1', '36.bm1.a1', '36.bp1.a1', '36.bx1.a1', '36.ck1.a1', '54.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2680, -1, 6856, -1, 6045, -1, 6811, -1], 'generators': [70957, 622537, 887131, 1651771, 811801, 793169], 'label': '1728.46354.18.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336085
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '9.c1.a1'], 'contains': ['36.bh1.a1', '36.bi1.a1', '36.bj1.a1', '36.bv1.a1', '36.bw1.a1', '36.bz1.a1', '36.ci1.a1', '54.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2580, -1, 7279, -1, 6372, -1, 7074, -1], 'generators': [70957, 622537, 887131, 1651771, 835777, 793169], 'label': '1728.46354.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336086
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.o1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.h1.a1', '36.p1.a1', '36.bc1.a1', '36.cl1.a1', '36.co1.a1', '36.cv1.a1', '36.dw1.a1', '36.dw1.b1', '36.eb1.a1', '36.eb1.b1', '54.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5907, -1, 5158, -1, 4829, -1, 4911, -1], 'generators': [46999, 887131, 622105, 1674451, 793169, 70633], 'label': '1728.46354.18.q1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336087
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.l1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.cm1.a1', '36.cx1.a1', '36.ec1.a1', '36.ec1.b1', '54.i1.a1', '72.br1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7439, -1, 3127, -1, 1984, -1, 2094, -1], 'generators': [46999, 70633, 887131, 1674451, 793169, 1341703], 'label': '1728.46354.18.r1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336088
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '6.p1.a1', '9.b1.a1'], 'contains': ['36.cm1.a1', '36.cr1.a1', '36.dj1.a1', '54.j1.a1', '72.bs1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5021, -1, 4193, -1, 2229, -1, 2727, -1], 'generators': [1674451, 70633, 887131, 835777, 1341703, 793169], 'label': '1728.46354.18.s1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336089
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.m1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.e1.a1', '36.f1.a1', '36.bb1.a1', '36.bd1.a1', '36.cl1.a1', '36.cs1.a1', '54.j1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3590, -1, 6135, -1, 5711, -1, 6080, -1], 'generators': [1674451, 622105, 793169, 835777, 887131, 70633], 'label': '1728.46354.18.t1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336090
    {'ambient': '1728.46354', 'aut_centralizer_order': 1, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 4, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '12.ch1.a1', '12.ci1.a1', '12.ck1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6644, -1, 5307, -1, 2538, -1, 3512, -1], 'generators': [46999, 622537, 1341703, 1674451, 622105, 835777, 793169], 'label': '1728.46354.4.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '4.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336091
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '6.q1.a1', '9.a1.a1'], 'contains': ['36.g1.a1', '36.i1.a1', '36.be1.a1', '36.bf1.a1', '36.cl1.a1', '36.cz1.a1', '36.dg1.a1', '54.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4747, -1, 6001, -1, 5444, -1, 5917, -1], 'generators': [834823, 622105, 887131, 1674451, 70633, 793169], 'label': '1728.46354.18.u1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336092
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '6.r1.a1', '9.b1.a1'], 'contains': ['36.cm1.a1', '36.dc1.a1', '36.dk1.a1', '54.k1.a1', '72.bw1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5702, -1, 3456, -1, 1949, -1, 2294, -1], 'generators': [834823, 70633, 887131, 1674451, 793169, 1341703], 'label': '1728.46354.18.v1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336093
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '6.s1.a1'], 'contains': ['36.cn1.a1', '36.dd1.a1', '36.dl1.a1', '54.k1.a1', '72.bx1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7291, -1, 2521, -1, 921, -1, 1379, -1], 'generators': [834823, 70633, 887131, 1674451, 793169, 766291], 'label': '1728.46354.18.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.w1.a1', 'old_label': '18.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336094
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.o1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '36.j1.a1', '36.n1.a1', '36.q1.a1', '36.bh1.a1', '36.cp1.a1', '36.cw1.a1', '36.dx1.a1', '36.dx1.b1', '36.ed1.a1', '36.ed1.b1', '54.i1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5948, -1, 5216, -1, 4690, -1, 5208, -1], 'generators': [46999, 622537, 887131, 1674451, 793169, 70633], 'label': '1728.46354.18.x1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336095
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.p1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '36.k1.a1', '36.l1.a1', '36.bg1.a1', '36.bi1.a1', '36.ct1.a1', '36.dh1.a1', '54.j1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3904, -1, 6099, -1, 5404, -1, 6267, -1], 'generators': [1674451, 622537, 793169, 835777, 887131, 70633], 'label': '1728.46354.18.y1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336096
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.r1.a1', '6.s1.a1', '9.c1.a1'], 'contains': ['36.a1.a1', '36.m1.a1', '36.o1.a1', '36.bj1.a1', '36.bk1.a1', '36.da1.a1', '36.di1.a1', '54.k1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4838, -1, 5327, -1, 4737, -1, 6006, -1], 'generators': [834823, 622537, 887131, 1674451, 70633, 793169], 'label': '1728.46354.18.z1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.z1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336097
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.v1.a1', '9.a1.a1'], 'contains': ['36.r1.a1', '36.u1.a1', '36.bn1.a1', '36.by1.a1', '36.co1.a1', '36.cs1.a1', '36.cz1.a1', '36.dy1.a1', '36.dy1.b1', '36.ee1.a1', '36.ee1.b1', '54.l1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5519, -1, 4787, -1, 4150, -1, 4107, -1], 'generators': [46999, 622105, 887131, 1634131, 793169, 70633], 'label': '1728.46354.18.ba1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336098
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.w1.a1', '9.c1.a1'], 'contains': ['36.s1.a1', '36.v1.a1', '36.bp1.a1', '36.bz1.a1', '36.cp1.a1', '36.ct1.a1', '36.da1.a1', '36.dz1.a1', '36.dz1.b1', '36.ef1.a1', '36.ef1.b1', '54.l1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5561, -1, 4881, -1, 3935, -1, 4265, -1], 'generators': [46999, 622537, 887131, 1634131, 793169, 70633], 'label': '1728.46354.18.bb1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336099
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.x1.a1'], 'contains': ['36.t1.a1', '36.w1.a1', '36.br1.a1', '36.ca1.a1', '36.cq1.a1', '36.cu1.a1', '36.db1.a1', '36.ea1.a1', '36.ea1.a2', '36.ea1.b1', '36.ea1.b2', '36.eg1.a1', '36.eg1.a2', '36.eg1.b1', '36.eg1.b2', '54.l1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7141, -1, 2465, -1, 3524, -1, 2919, -1], 'generators': [46999, 47089, 887131, 1634131, 793169, 70633], 'label': '1728.46354.18.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '18.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336100
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.u1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.x1.a1', '36.y1.a1', '36.cf1.a1', '36.ch1.a1', '36.co1.a1', '36.dg1.a1', '54.m1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2976, -1, 6237, -1, 5598, -1, 6040, -1], 'generators': [46999, 622105, 887131, 835777, 70633, 793169], 'label': '1728.46354.18.bd1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336101
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 6, 'centralizer': '288.a1.a1', 'complements': ['864.g1.a1', '864.i1.a1', '864.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.i1.a1', '4.i1.b1', '6.a1.a1', '6.l1.a1', '6.o1.a1', '8.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7646, 6357, 3127, 3388, 2111, 6302, 2174, 7090], 'generators': [46999, 1341703, 622537, 1674451, 622105, 70633, 887131, 793169], 'label': '1728.46354.2.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.d1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '864.4673', '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': '288.1028'}
  • id: 264336102
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.l1.a1', '12.cp1.a1', '12.cq1.a1', '12.cr1.a1', '16.i1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9200, -1, 1208, -1, 1546, -1, 1662, -1], 'generators': [46999, 887131, 622537, 1674451, 70633, 622105, 1341703], 'label': '1728.46354.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336103
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.y1.a1', '9.c1.a1'], 'contains': ['36.z1.a1', '36.ba1.a1', '36.ci1.a1', '36.ck1.a1', '36.cp1.a1', '36.dh1.a1', '36.di1.a1', '54.m1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2097, -1, 5967, -1, 5357, -1, 6188, -1], 'generators': [46999, 887131, 793169, 835777, 70633, 622537], 'label': '1728.46354.18.be1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336104
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.w1.a1', '6.x1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.cr1.a1', '36.dc1.a1', '36.eh1.a1', '36.eh1.b1', '54.l1.a1', '72.co1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7392, -1, 2230, -1, 1307, -1, 1301, -1], 'generators': [46999, 70633, 887131, 1634131, 793169, 1341703], 'label': '1728.46354.18.bf1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336105
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '18.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.y1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.dj1.a1', '36.dk1.a1', '54.m1.a1', '72.cp1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4580, -1, 5561, -1, 2729, -1, 3181, -1], 'generators': [46999, 70633, 887131, 835777, 793169, 1341703], 'label': '1728.46354.18.bg1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336106
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1.a1', '6.ba1.a1', '9.b1.a1'], 'contains': ['36.cr1.a1', '36.cx1.a1', '36.dk1.a1', '54.n1.a1', '72.cy1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5738, -1, 5505, -1, 2815, -1, 3446, -1], 'generators': [834823, 70633, 887131, 1634131, 793169, 1341703], 'label': '1728.46354.18.bh1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336107
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1.a1', '6.bb1.a1', '9.a1.a1'], 'contains': ['36.bl1.a1', '36.bo1.a1', '36.bs1.a1', '36.cb1.a1', '36.cs1.a1', '36.cv1.a1', '36.dg1.a1', '54.n1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4777, -1, 6260, -1, 5561, -1, 5943, -1], 'generators': [834823, 622105, 887131, 1634131, 70633, 793169], 'label': '1728.46354.18.bi1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336108
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.ba1.a1', '6.bb1.a1', '9.c1.a1'], 'contains': ['36.bm1.a1', '36.bq1.a1', '36.bv1.a1', '36.cc1.a1', '36.ct1.a1', '36.cw1.a1', '36.di1.a1', '54.n1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4802, -1, 6073, -1, 5317, -1, 6154, -1], 'generators': [834823, 622537, 887131, 1634131, 70633, 793169], 'label': '1728.46354.18.bj1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336109
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bc1.a1', '6.bd1.a1', '6.be1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.bt1.a1', '36.bu1.a1', '36.cd1.a1', '36.cg1.a1', '36.cv1.a1', '36.cz1.a1', '54.o1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5237, -1, 5350, -1, 5480, -1, 5973, -1], 'generators': [1675405, 622105, 887131, 835777, 70633, 793169], 'label': '1728.46354.18.bk1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336110
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bl1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bc1.a1', '6.bf1.a1', '9.c1.a1'], 'contains': ['36.bw1.a1', '36.bx1.a1', '36.ce1.a1', '36.cj1.a1', '36.cw1.a1', '36.da1.a1', '36.dh1.a1', '54.o1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4869, -1, 5764, -1, 5252, -1, 6226, -1], 'generators': [1675405, 622537, 887131, 835777, 70633, 793169], 'label': '1728.46354.18.bl1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336111
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '18.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1.a1', '6.bf1.a1', '9.b1.a1'], 'contains': ['36.cx1.a1', '36.dc1.a1', '36.dj1.a1', '54.o1.a1', '72.dh1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6777, -1, 4163, -1, 2599, -1, 3667, -1], 'generators': [1675405, 70633, 887131, 835777, 793169, 1341703], 'label': '1728.46354.18.bm1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336112
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '18.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.be1.a1', '6.bf1.a1'], 'contains': ['36.cy1.a1', '36.de1.a1', '36.dm1.a1', '54.o1.a1', '72.di1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8001, -1, 2917, -1, 2260, -1, 5137, -1], 'generators': [1675405, 70633, 887131, 835777, 793169, 767155], 'label': '1728.46354.18.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1.a1', 'old_label': '18.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336113
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.j1.a1', '8.l1.a1', '12.cp1.b1', '12.cq1.b1', '12.cr1.b1', '16.i1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9200, -1, 2207, -1, 1546, -1, 1709, -1], 'generators': [793511, 887131, 622537, 1674451, 70633, 622105, 1341703], 'label': '1728.46354.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.i1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336114
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.e1.a1', '12.g1.a1', '12.bn1.a1', '12.bs1.a1', '12.bv1.a1', '12.cc1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.bu1.a1', '72.a1.a1', '72.b1.a1', '72.bm1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5134, 6395, 5470, 3403, 3974, 6398, 4319, 3969], 'generators': [793169, 622105, 887131, 70633, 622537], 'label': '1728.46354.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.e1.a1', '12.g1.a1'], 'normal_contains': ['48.d1.a1', '72.a1.a1', '72.b1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336115
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.h1.a1', '12.i1.a1', '12.bl1.a1', '12.bp1.a1', '12.bt1.a1', '12.bw1.a1'], 'contains': ['48.e1.a1', '72.a1.a1', '72.c1.a1', '72.bn1.a1', '96.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7811, 2550, 3209, 7989, 1702, 3373, 1575, 5332], 'generators': [793169, 70633, 1341703, 622105, 887131], 'label': '1728.46354.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1', '12.h1.a1', '12.i1.a1'], 'normal_contains': ['48.e1.a1', '72.a1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '864.4673', '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': '48.48'}
  • id: 264336116
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1', '12.f1.a1', '12.bq1.a1', '12.by1.a1', '12.ce1.a1', '12.cf1.a1'], 'contains': ['48.f1.a1', '72.b1.a1', '72.c1.a1', '72.bo1.a1', '96.d1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7044, 4454, 2624, 4903, 1301, 4782, 1999, 5939], 'generators': [793169, 70633, 1341703, 622537, 887131], 'label': '1728.46354.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1', '12.f1.a1'], 'normal_contains': ['48.f1.a1', '72.b1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '864.4673', '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': '48.48'}
  • id: 264336176
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.be1.a1', '8.i1.a1'], 'contains': ['48.u1.a1', '48.z1.a1', '48.bi1.a1', '72.dc1.a1', '72.di1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8325, -1, 2967, -1, 2417, -1, 5520, -1], 'generators': [1675405, 622105, 835777, 793169, 767155], 'label': '1728.46354.24.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '24.cd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336117
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '36.b1.a1', 'complements': ['72.d1.a1', '72.d1.b1', '72.fm1.a1', '72.fn1.a1', '72.fr1.a1', '72.ft1.a1', '72.fs1.a1', '72.fu1.a2', '72.fu1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.k1.a1', '12.ci1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.bt1.a1', '72.bz1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4317, 9110, 7020, 1214, 8421, 8709, 8564, 1729], 'generators': [1674451, 622105, 835777, 793169, 622537], 'label': '1728.46354.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['6.b1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336118
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.a1.a1', 'complements': ['72.bz1.a1', '72.cv1.a1', '72.ca1.a1', '72.cu1.a1', '72.cw1.a1', '72.df1.a1', '72.dg1.a1', '72.di1.a1', '72.cb1.a1', '72.dp1.a1', '72.cx1.a1', '72.da1.a1', '72.de1.a1', '72.dr1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.cp1.a1', '12.ct1.a1'], 'contains': ['48.e1.a1', '72.d1.a1', '72.fd1.a1', '96.o1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9240, 317, 1133, 9485, 868, 1370, 856, 9074], 'generators': [46999, 70633, 622105, 1341703, 887131], 'label': '1728.46354.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1'], 'normal_contains': ['48.e1.a1', '72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336119
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.a1.a1', 'complements': ['72.bz1.a1', '72.cv1.a1', '72.ca1.a1', '72.cu1.a1', '72.cw1.a1', '72.df1.a1', '72.dg1.a1', '72.di1.a1', '72.cb1.a1', '72.dp1.a1', '72.cx1.a1', '72.da1.a1', '72.de1.a1', '72.dr1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.cp1.b1', '12.ct1.b1'], 'contains': ['48.e1.a1', '72.d1.b1', '72.fd1.b1', '96.o1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9240, 317, 1102, 8831, 868, 1370, 916, 7252], 'generators': [793511, 70633, 622105, 1341703, 887131], 'label': '1728.46354.24.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.b1.b1', '12.c1.a1'], 'normal_contains': ['48.e1.a1', '72.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336120
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.c1.a1', 'complements': ['72.bt1.a1', '72.cr1.a1', '72.bu1.a1', '72.cq1.a1', '72.cs1.a1', '72.dc1.a1', '72.dd1.a1', '72.bv1.a1', '72.do1.a1', '72.ct1.a1', '72.bx1.a1', '72.cz1.a1', '72.db1.a1', '72.dq1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1', '12.cr1.a1', '12.cu1.a1'], 'contains': ['48.f1.a1', '72.d1.a1', '72.fe1.a1', '96.p1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8851, 1587, 1022, 6584, 821, 2721, 976, 9681], 'generators': [46999, 70633, 622537, 1341703, 887131], 'label': '1728.46354.24.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.b1.a1', '12.d1.a1'], 'normal_contains': ['48.f1.a1', '72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336121
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.c1.a1', 'complements': ['72.bt1.a1', '72.cr1.a1', '72.bu1.a1', '72.cq1.a1', '72.cs1.a1', '72.dc1.a1', '72.dd1.a1', '72.bv1.a1', '72.do1.a1', '72.ct1.a1', '72.bx1.a1', '72.cz1.a1', '72.db1.a1', '72.dq1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.d1.a1', '12.cr1.b1', '12.cu1.b1'], 'contains': ['48.f1.a1', '72.d1.b1', '72.fe1.b1', '96.p1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8851, 1587, 1081, 5930, 821, 2721, 1176, 7859], 'generators': [793511, 70633, 622537, 1341703, 887131], 'label': '1728.46354.24.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': ['8.b1.b1', '12.d1.a1'], 'normal_contains': ['48.f1.a1', '72.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.b1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336122
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1', '12.n1.a1', '12.o1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.o1.a1', '48.bm1.a1', '48.bv1.a1', '72.e1.a1', '72.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3683, -1, 7621, -1, 8226, -1, 8179, -1], 'generators': [1674451, 622537, 793169, 887131, 622105], 'label': '1728.46354.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336123
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1', '12.t1.a1', '12.bn1.a1'], 'contains': ['48.g1.a1', '48.k1.a1', '48.bn1.a1', '48.bw1.a1', '48.bw1.b1', '72.g1.a1', '72.h1.a1', '72.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2692, -1, 6953, -1, 7955, -1, 7713, -1], 'generators': [46999, 622105, 793169, 887131, 622537], 'label': '1728.46354.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336124
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.m1.a1', '12.cs1.a1', '12.ct1.a1', '12.cu1.a1', '12.cv1.a1', '12.cv1.a2', '16.j1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8774, -1, 967, -1, 770, -1, 791, -1], 'generators': [46999, 887131, 622105, 1634131, 70633, 1341703, 622537], 'label': '1728.46354.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
  • id: 264336125
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.p1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1'], 'contains': ['48.g1.a1', '48.o1.a1', '48.bo1.a1', '48.bx1.a1', '72.j1.a1', '72.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2044, -1, 6627, -1, 7557, -1, 7979, -1], 'generators': [1651771, 622537, 793169, 887131, 622105], 'label': '1728.46354.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336126
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.k1.a1', '12.q1.a1', '12.u1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.w1.a1', '48.bp1.a1', '48.by1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3772, -1, 8071, -1, 7770, -1, 8097, -1], 'generators': [1634131, 622105, 793169, 887131, 622537], 'label': '1728.46354.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336127
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.v1.a1', '12.z1.a1', '12.bc1.a1', '12.bd1.a1', '12.be1.a1', '12.bs1.a1'], 'contains': ['48.g1.a1', '48.s1.a1', '48.bq1.a1', '48.bz1.a1', '72.o1.a1', '72.p1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2989, -1, 8214, -1, 8282, -1, 8298, -1], 'generators': [1675405, 622537, 793169, 887131, 622105], 'label': '1728.46354.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336128
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.l1.a1', '12.r1.a1', '12.w1.a1', '12.bc1.a1', '12.bf1.a1', '12.bg1.a1'], 'contains': ['48.g1.a1', '48.w1.a1', '48.br1.a1', '48.ca1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3128, -1, 6788, -1, 7244, -1, 7596, -1], 'generators': [1656811, 622105, 793169, 887131, 622537], 'label': '1728.46354.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336129
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.q1.a1', '12.x1.a1', '12.bd1.a1', '12.bf1.a1', '12.bh1.a1', '12.bv1.a1'], 'contains': ['48.g1.a1', '48.x1.a1', '48.bs1.a1', '48.cb1.a1', '72.t1.a1', '72.u1.a1', '72.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2211, -1, 7517, -1, 7909, -1, 7899, -1], 'generators': [1633789, 622105, 793169, 887131, 622537], 'label': '1728.46354.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336130
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.k1.a1', '12.s1.a1', '12.w1.a1', '12.bd1.a1', '12.bi1.a1', '12.bj1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.be1.a1', '72.w1.a1', '72.bd1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1385, -1, 7042, -1, 8175, -1, 8418, -1], 'generators': [835777, 622105, 887131, 622537, 793169], 'label': '1728.46354.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336131
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.v1.a1', '12.ba1.a1', '12.bf1.a1', '12.bi1.a1', '12.bk1.a1', '12.bn1.a1'], 'contains': ['48.g1.a1', '48.cc1.a1', '48.cc1.b1', '72.x1.a1', '72.be1.a1', '72.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2283, -1, 7435, -1, 6234, -1, 5999, -1], 'generators': [70957, 887131, 793169, 622537, 622105], 'label': '1728.46354.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336132
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.l1.a1', '12.t1.a1', '12.u1.a1', '12.be1.a1', '12.bh1.a1', '12.bk1.a1'], 'contains': ['48.g1.a1', '48.be1.a1', '72.y1.a1', '72.bf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2384, -1, 7761, -1, 7862, -1, 8058, -1], 'generators': [811801, 622105, 887131, 622537, 793169], 'label': '1728.46354.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336133
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.s1.a1', '12.y1.a1', '12.z1.a1', '12.bg1.a1', '12.bk1.a1', '12.cc1.a1'], 'contains': ['48.g1.a1', '48.bf1.a1', '72.z1.a1', '72.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1129, -1, 6979, -1, 8088, -1, 8137, -1], 'generators': [834823, 622105, 887131, 622537, 793169], 'label': '1728.46354.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336134
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.p1.a1', '12.bb1.a1', '12.bg1.a1', '12.bh1.a1', '12.bj1.a1', '12.bs1.a1'], 'contains': ['48.g1.a1', '48.cd1.a1', '72.ba1.a1', '72.bh1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4115, -1, 6754, -1, 6467, -1, 6912, -1], 'generators': [1651447, 622537, 793169, 622105, 887131], 'label': '1728.46354.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336135
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.b1', '8.k1.a1', '8.m1.a1', '12.cs1.b1', '12.ct1.b1', '12.cu1.b1', '12.cv1.b1', '12.cv1.b2', '16.j1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8774, -1, 625, -1, 770, -1, 936, -1], 'generators': [793511, 887131, 622105, 1634131, 70633, 1341703, 622537], 'label': '1728.46354.4.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
  • id: 264336136
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.t1.a1', '12.x1.a1', '12.bb1.a1', '12.bc1.a1', '12.bi1.a1', '12.cc1.a1'], 'contains': ['48.g1.a1', '48.bt1.a1', '72.bb1.a1', '72.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2891, -1, 8184, -1, 7722, -1, 7860, -1], 'generators': [812125, 622105, 887131, 622537, 1633643], 'label': '1728.46354.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336137
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.r1.a1', '12.y1.a1', '12.ba1.a1', '12.be1.a1', '12.bj1.a1', '12.bv1.a1'], 'contains': ['48.g1.a1', '48.ce1.a1', '72.bc1.a1', '72.bj1.a1', '72.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4080, -1, 6583, -1, 6514, -1, 6262, -1], 'generators': [1656487, 622105, 793169, 887131, 622537], 'label': '1728.46354.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336138
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bu1.a1', '12.bx1.a1', '12.cd1.a1'], 'contains': ['48.cf1.a1', '72.a1.a1', '72.bo1.a1', '72.bp1.a1', '96.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9106, -1, 1957, -1, 1152, -1, 2274, -1], 'generators': [793169, 70633, 767155, 622105, 887131], 'label': '1728.46354.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '24.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336139
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bm1.a1', '12.bz1.a1', '12.cg1.a1'], 'contains': ['48.cg1.a1', '72.b1.a1', '72.bn1.a1', '72.bp1.a1', '96.e1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8300, -1, 1305, -1, 232, -1, 946, -1], 'generators': [793169, 70633, 766291, 622537, 887131], 'label': '1728.46354.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336140
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bo1.a1', '12.br1.a1', '12.ca1.a1'], 'contains': ['48.ch1.a1', '72.c1.a1', '72.bm1.a1', '72.bp1.a1', '96.f1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8510, -1, 867, -1, 503, -1, 530, -1], 'generators': [793169, 70633, 1341703, 47089, 887131], 'label': '1728.46354.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336141
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.cb1.a1'], 'contains': ['48.ci1.a1', '72.bm1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '96.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8588, -1, 1326, -1, 404, -1, 787, -1], 'generators': [793169, 70633, 766291, 47089, 887131], 'label': '1728.46354.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '24.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336142
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '8.c1.a1', '12.ch1.a1'], 'contains': ['48.h1.a1', '48.l1.a1', '48.t1.a1', '48.cj1.a1', '48.cj1.b1', '72.bq1.a1', '72.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8399, -1, 3285, -1, 2329, -1, 2162, -1], 'generators': [46999, 1341703, 1674451, 793169, 622105], 'label': '1728.46354.24.y1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336143
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '8.d1.a1', '12.ch1.a1'], 'contains': ['48.h1.a1', '48.p1.a1', '48.bg1.a1', '72.bs1.a1', '72.bt1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5049, -1, 4363, -1, 2222, -1, 3318, -1], 'generators': [1674451, 622105, 835777, 1341703, 793169], 'label': '1728.46354.24.z1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336144
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '8.e1.a1', '12.ch1.a1'], 'contains': ['48.h1.a1', '48.y1.a1', '48.bh1.a1', '72.bv1.a1', '72.bw1.a1', '72.bx1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6860, -1, 3484, -1, 1956, -1, 2126, -1], 'generators': [834823, 622105, 1674451, 793169, 1341703], 'label': '1728.46354.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336145
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.j1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.s1.a1', '48.ck1.a1', '48.ck1.b1', '72.bq1.a1', '72.by1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3732, -1, 9379, -1, 9224, -1, 9073, -1], 'generators': [46999, 622537, 1674451, 793169, 622105], 'label': '1728.46354.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336146
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.a1.a1', 'complements': ['288.y1.a1', '288.bf1.a1', '288.ba1.a2', '288.bh1.a1', '288.ba1.a1', '288.bh1.a2', '288.bi1.a1', '288.bm1.a1', '288.bk1.a2', '288.bo1.a2', '288.bk1.a1', '288.bo1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.f1.a1', '12.cr1.a1', '12.cr1.b1', '18.r1.a1', '18.x1.a1', '24.bc1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7367, 6033, 2866, 3905, 2054, 6360, 2217, 7945], 'generators': [46999, 887131, 622537, 1674451, 70633, 793169, 1341703], 'label': '1728.46354.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1', '12.d1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '864.4673', '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': '288.1028'}
  • id: 264336147
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '8.c1.a1', '12.ck1.a1'], 'contains': ['48.i1.a1', '48.m1.a1', '48.v1.a1', '48.cl1.a1', '48.cl1.b1', '72.br1.a1', '72.by1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7545, -1, 2758, -1, 2114, -1, 2211, -1], 'generators': [46999, 622537, 1674451, 793169, 1341703], 'label': '1728.46354.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336148
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '8.d1.a1', '12.ck1.a1'], 'contains': ['48.i1.a1', '48.q1.a1', '48.bj1.a1', '72.bs1.a1', '72.bz1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5009, -1, 4320, -1, 2178, -1, 3355, -1], 'generators': [1674451, 622537, 835777, 1341703, 793169], 'label': '1728.46354.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336149
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.l1.a1', '12.cj1.a1'], 'contains': ['48.a1.a1', '48.w1.a1', '48.be1.a1', '72.bu1.a1', '72.ca1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3179, -1, 8125, -1, 9181, -1, 9011, -1], 'generators': [1674451, 622105, 1674955, 793169, 622537], 'label': '1728.46354.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336150
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.m1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.a1.a1', '48.x1.a1', '48.bf1.a1', '72.bv1.a1', '72.cb1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1212, -1, 7552, -1, 8708, -1, 8702, -1], 'generators': [834823, 622105, 1674451, 793169, 622537], 'label': '1728.46354.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336151
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '8.e1.a1', '12.ck1.a1'], 'contains': ['48.i1.a1', '48.ba1.a1', '48.bk1.a1', '72.bw1.a1', '72.cb1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5652, -1, 3502, -1, 1987, -1, 2539, -1], 'generators': [834823, 622537, 1674451, 793169, 1341703], 'label': '1728.46354.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336152
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '8.e1.a1'], 'contains': ['48.j1.a1', '48.bb1.a1', '48.bl1.a1', '72.bx1.a1', '72.cb1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7416, -1, 2532, -1, 697, -1, 1349, -1], 'generators': [834823, 622537, 1674451, 793169, 766291], 'label': '1728.46354.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1.a1', 'old_label': '24.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336153
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.cl1.a1', '12.cm1.a1'], 'contains': ['48.k1.a1', '48.o1.a1', '48.s1.a1', '48.cm1.a1', '48.cm1.b1', '72.cc1.a1', '72.cd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [986, -1, 9787, -1, 9611, -1, 9455, -1], 'generators': [46999, 622537, 835273, 793169, 622105], 'label': '1728.46354.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336154
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.q1.a1', '12.ci1.a1', '12.cl1.a1'], 'contains': ['48.b1.a1', '48.k1.a1', '48.x1.a1', '48.cn1.a1', '48.cn1.b1', '72.ce1.a1', '72.cf1.a1', '72.cg1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3562, -1, 9047, -1, 8506, -1, 8457, -1], 'generators': [46999, 622105, 1634131, 793169, 622537], 'label': '1728.46354.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336155
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.cj1.a1', '12.cm1.a1'], 'contains': ['48.k1.a1', '48.w1.a1', '48.x1.a1', '48.co1.a1', '48.co1.b1', '72.ch1.a1', '72.ci1.a1', '72.cj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1071, -1, 9426, -1, 9050, -1, 8927, -1], 'generators': [46999, 622105, 793657, 793169, 622537], 'label': '1728.46354.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336156
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.s1.a1', '12.ci1.a1', '12.cm1.a1'], 'contains': ['48.c1.a1', '48.k1.a1', '48.bf1.a1', '72.ck1.a1', '72.cm1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1169, -1, 7105, -1, 8834, -1, 8888, -1], 'generators': [46999, 622105, 835777, 622537, 793169], 'label': '1728.46354.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336157
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': ['288.u1.a1', '288.u1.b1', '288.bd1.a1', '288.be1.a1', '288.bl1.a1', '288.bn1.a1', '288.bm1.a1', '288.bo1.a2', '288.bo1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.g1.a1', '12.k1.a1', '12.l1.a1', '12.u1.a1', '12.w1.a1', '18.t1.a1', '18.y1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3534, 8677, 6109, 874, 5726, 9539, 6365, 430], 'generators': [1674451, 622537, 793169, 835777, 622105, 887131, 70633], 'label': '1728.46354.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.e1.a1', '12.g1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336158
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '12.cj1.a1', '12.cl1.a1'], 'contains': ['48.k1.a1', '48.be1.a1', '48.bf1.a1', '72.cl1.a1', '72.cn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [561, -1, 9455, -1, 9305, -1, 9115, -1], 'generators': [46999, 622105, 1674955, 622537, 793169], 'label': '1728.46354.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336159
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '8.f1.a1', '12.ch1.a1'], 'contains': ['48.l1.a1', '48.p1.a1', '48.y1.a1', '48.cp1.a1', '48.cp1.b1', '72.ce1.a1', '72.co1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7606, -1, 2721, -1, 1653, -1, 1608, -1], 'generators': [46999, 622105, 1634131, 793169, 1341703], 'label': '1728.46354.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336160
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '8.f1.a1', '12.ck1.a1'], 'contains': ['48.m1.a1', '48.q1.a1', '48.ba1.a1', '48.cq1.a1', '48.cq1.b1', '72.cf1.a1', '72.co1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7340, -1, 2319, -1, 1556, -1, 1910, -1], 'generators': [46999, 622537, 1634131, 793169, 1341703], 'label': '1728.46354.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.bo1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336161
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.x1.a1', '8.f1.a1'], 'contains': ['48.n1.a1', '48.r1.a1', '48.bc1.a1', '48.cr1.a1', '48.cr1.a2', '48.cr1.b1', '48.cr1.b2', '72.cg1.a1', '72.co1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8547, -1, 954, -1, 964, -1, 1061, -1], 'generators': [46999, 47089, 1634131, 793169, 1341703], 'label': '1728.46354.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '24.bp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336162
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.g1.a1', '12.ch1.a1'], 'contains': ['48.l1.a1', '48.bg1.a1', '48.bh1.a1', '72.ck1.a1', '72.cp1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4716, -1, 5828, -1, 2932, -1, 3575, -1], 'generators': [46999, 622105, 835777, 793169, 1341703], 'label': '1728.46354.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '24.bq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336163
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1.a1', '8.g1.a1', '12.ck1.a1'], 'contains': ['48.m1.a1', '48.bj1.a1', '48.bk1.a1', '72.cm1.a1', '72.cp1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4681, -1, 5605, -1, 2762, -1, 3650, -1], 'generators': [46999, 1341703, 835777, 622537, 793169], 'label': '1728.46354.24.br1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.br1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336164
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.u1.a1', '12.cl1.a1'], 'contains': ['48.b1.a1', '48.o1.a1', '48.be1.a1', '72.cq1.a1', '72.cu1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2098, -1, 8979, -1, 9120, -1, 8986, -1], 'generators': [835273, 622105, 1674955, 793169, 622537], 'label': '1728.46354.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336165
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.w1.a1', '12.cm1.a1'], 'contains': ['48.c1.a1', '48.o1.a1', '48.w1.a1', '72.cr1.a1', '72.cv1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1288, -1, 8143, -1, 9151, -1, 8961, -1], 'generators': [835273, 622105, 835777, 793169, 622537], 'label': '1728.46354.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bt1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336166
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.u1.a1', '12.w1.a1'], 'contains': ['48.o1.a1', '48.w1.a1', '48.be1.a1', '72.cs1.a1', '72.cw1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2120, -1, 8047, -1, 9090, -1, 8806, -1], 'generators': [1651771, 622105, 1674955, 793169, 622537], 'label': '1728.46354.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336167
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.cl1.a1', '12.cm1.a1'], 'contains': ['48.o1.a1', '48.x1.a1', '48.bf1.a1', '72.ct1.a1', '72.cx1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [90, -1, 9077, -1, 9268, -1, 9036, -1], 'generators': [834823, 622105, 835273, 793169, 622537], 'label': '1728.46354.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336168
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '288.b1.a1', 'complements': ['288.q1.a1', '288.w1.a1', '288.bc1.a1', '288.be1.a1', '288.z1.a1', '288.bg1.a1', '288.ba1.a2', '288.bh1.a1', '288.ba1.a1', '288.bh1.a2', '288.bj1.a1', '288.bn1.a1', '288.bk1.a2', '288.bo1.a2', '288.bk1.a1', '288.bo1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.i1.a1', '18.bd1.a1', '18.bg1.a1', '24.bq1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4624, 1339, 5613, 8327, 2861, 357, 3379, 7099], 'generators': [46999, 887131, 622105, 835777, 70633, 793169, 1341703], 'label': '1728.46354.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['12.c1.a1', '12.h1.a1', '12.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336169
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1.a1', '8.h1.a1', '12.ch1.a1'], 'contains': ['48.p1.a1', '48.t1.a1', '48.bh1.a1', '72.cy1.a1', '72.cz1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6707, -1, 5644, -1, 2897, -1, 3621, -1], 'generators': [834823, 622105, 1634131, 793169, 1341703], 'label': '1728.46354.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.bw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336170
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.ba1.a1', '8.h1.a1', '12.ck1.a1'], 'contains': ['48.q1.a1', '48.v1.a1', '48.bk1.a1', '72.cy1.a1', '72.da1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5731, -1, 5546, -1, 2809, -1, 4505, -1], 'generators': [834823, 622537, 1634131, 793169, 1341703], 'label': '1728.46354.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.bx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336171
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.z1.a1', '12.ci1.a1', '12.cl1.a1'], 'contains': ['48.b1.a1', '48.s1.a1', '48.bf1.a1', '72.cz1.a1', '72.da1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2540, -1, 8100, -1, 8872, -1, 8831, -1], 'generators': [834823, 622105, 1634131, 793169, 622537], 'label': '1728.46354.24.by1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.by1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336172
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '12.cj1.a1', '12.cm1.a1'], 'contains': ['48.s1.a1', '48.w1.a1', '48.bf1.a1', '72.db1.a1', '72.de1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1041, -1, 9095, -1, 9418, -1, 9171, -1], 'generators': [834823, 622105, 793657, 793169, 622537], 'label': '1728.46354.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336173
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.bd1.a1', '12.ci1.a1', '12.cm1.a1'], 'contains': ['48.c1.a1', '48.s1.a1', '48.x1.a1', '72.dc1.a1', '72.df1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1457, -1, 8812, -1, 8677, -1, 8856, -1], 'generators': [1675405, 622105, 835777, 793169, 622537], 'label': '1728.46354.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.ca1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336174
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '12.cj1.a1', '12.cl1.a1'], 'contains': ['48.s1.a1', '48.x1.a1', '48.be1.a1', '72.dd1.a1', '72.dg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1019, -1, 9744, -1, 9343, -1, 9146, -1], 'generators': [1675405, 622105, 1674955, 793169, 622537], 'label': '1728.46354.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.cb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336175
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1.a1', '8.i1.a1', '12.ch1.a1'], 'contains': ['48.t1.a1', '48.y1.a1', '48.bg1.a1', '72.dc1.a1', '72.dh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6897, -1, 4223, -1, 2680, -1, 4471, -1], 'generators': [1675405, 622105, 835777, 793169, 1341703], 'label': '1728.46354.24.cc1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '24.cc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336177
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bf1.a1', '8.i1.a1', '12.ck1.a1'], 'contains': ['48.v1.a1', '48.ba1.a1', '48.bj1.a1', '72.df1.a1', '72.dh1.a1', '72.di1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6801, -1, 3575, -1, 2505, -1, 4568, -1], 'generators': [1675405, 622537, 835777, 793169, 1341703], 'label': '1728.46354.24.ce1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '24.ce1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336178
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.bm1.a1', '48.bn1.a1', '48.bq1.a1', '48.ck1.a1', '48.ck1.b1', '48.cm1.a1', '48.cm1.b1', '72.dj1.a1', '72.dk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3456, -1, 9718, -1, 9704, -1, 9672, -1], 'generators': [46999, 622537, 1674451, 1633643, 622105], 'label': '1728.46354.24.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.cf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336179
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.j1.a1', '12.k1.a1', '12.m1.a1', '12.q1.a1', '12.s1.a1', '12.z1.a1', '12.bd1.a1', '12.ci1.a1', '12.cj1.a1', '12.cl1.a1', '12.cm1.a1', '18.a1.a1', '18.e1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1854, -1, 7698, -1, 8211, -1, 8298, -1], 'generators': [46999, 622537, 793169, 1674451, 622105, 835777, 887131], 'label': '1728.46354.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.a1', 'projective_image': '864.4673', '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': '72.46'}
  • id: 264336180
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1'], 'contains': ['48.bn1.a1', '48.bp1.a1', '48.bs1.a1', '48.cn1.a1', '48.cn1.b1', '48.co1.a1', '48.co1.b1', '72.dl1.a1', '72.dm1.a1', '72.dn1.a1', '72.dn1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2749, -1, 9347, -1, 9000, -1, 8735, -1], 'generators': [46999, 622105, 1634131, 1633643, 622537], 'label': '1728.46354.24.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '24.cg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336181
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1'], 'contains': ['48.bo1.a1', '48.bs1.a1', '48.bt1.a1', '72.do1.a1', '72.dp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1683, -1, 9198, -1, 9538, -1, 9381, -1], 'generators': [812125, 622105, 1651771, 1633643, 622537], 'label': '1728.46354.24.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '24.ch1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336182
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1'], 'contains': ['48.bq1.a1', '48.br1.a1', '48.bt1.a1', '72.dq1.a1', '72.dr1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2949, -1, 9239, -1, 9568, -1, 9411, -1], 'generators': [812125, 622105, 1656811, 1633643, 622537], 'label': '1728.46354.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '24.ci1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336183
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.cn1.a1', '12.cn1.b1'], 'contains': ['48.bm1.a1', '48.bo1.a1', '48.bu1.a1', '48.bv1.a1', '48.bx1.a1', '72.ds1.a1', '72.dt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5495, -1, 5031, -1, 4895, -1, 5231, -1], 'generators': [1674451, 622537, 817145, 887131, 622105], 'label': '1728.46354.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336184
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.cn1.a1', '12.co1.a1'], 'contains': ['48.bu1.a1', '48.bw1.a1', '48.cc1.b1', '72.du1.a1', '72.dv1.a1', '72.dw1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6276, -1, 4521, -1, 4066, -1, 4183, -1], 'generators': [46999, 887131, 817145, 622537, 622105], 'label': '1728.46354.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.ck1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336185
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.cn1.b1', '12.co1.b1'], 'contains': ['48.bu1.a1', '48.bw1.b1', '48.cc1.a1', '72.du1.b1', '72.dv1.b1', '72.dw1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6276, -1, 4587, -1, 4066, -1, 4249, -1], 'generators': [70957, 887131, 817145, 622537, 622105], 'label': '1728.46354.24.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.ck1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336186
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.co1.a1', '12.co1.b1'], 'contains': ['48.bp1.a1', '48.br1.a1', '48.bu1.a1', '48.by1.a1', '48.ca1.a1', '72.dx1.a1', '72.dy1.a1', '72.dz1.a1', '72.dz1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5433, -1, 4158, -1, 4020, -1, 4023, -1], 'generators': [1634131, 622105, 817145, 887131, 622537], 'label': '1728.46354.24.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336187
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.cn1.a1', '12.cn1.b1'], 'contains': ['48.bu1.a1', '48.bz1.a1', '48.cd1.a1', '72.ea1.a1', '72.eb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6243, -1, 4889, -1, 4538, -1, 5019, -1], 'generators': [1675405, 622537, 817145, 622105, 887131], 'label': '1728.46354.24.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336188
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '12.co1.a1', '12.co1.b1'], 'contains': ['48.bu1.a1', '48.cb1.a1', '48.ce1.a1', '72.ec1.a1', '72.ed1.a1', '72.ee1.a1', '72.ee1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5791, -1, 3851, -1, 3474, -1, 3681, -1], 'generators': [1633789, 622105, 817145, 887131, 622537], 'label': '1728.46354.24.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336189
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.cn1.a1', '12.cq1.a1'], 'contains': ['48.bv1.a1', '48.bw1.a1', '48.bz1.a1', '48.ck1.a1', '48.cm1.a1', '72.ef1.a1', '72.eh1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6332, -1, 5064, -1, 5324, -1, 5420, -1], 'generators': [46999, 622537, 1674451, 887131, 622105], 'label': '1728.46354.24.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.co1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336190
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.j1.a1', '12.l1.a1', '12.o1.a1', '12.r1.a1', '12.t1.a1', '12.bc1.a1', '12.be1.a1', '18.b1.a1', '18.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3147, -1, 7750, -1, 7121, -1, 7265, -1], 'generators': [46999, 622537, 887131, 1674451, 622105, 811801, 793169], 'label': '1728.46354.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '864.4673', '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': '144.192'}
  • id: 264336191
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.cn1.b1', '12.cq1.b1'], 'contains': ['48.bv1.a1', '48.bw1.b1', '48.bz1.a1', '48.ck1.b1', '48.cm1.b1', '72.ef1.b1', '72.eh1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6332, -1, 4962, -1, 5324, -1, 5467, -1], 'generators': [793511, 622537, 1674451, 887131, 622105], 'label': '1728.46354.24.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.co1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336192
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.cn1.b1', '12.cq1.a1'], 'contains': ['48.bv1.a1', '48.cc1.a1', '48.cd1.a1', '72.eg1.a1', '72.ei1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6659, -1, 4706, -1, 4280, -1, 4982, -1], 'generators': [70957, 622537, 1674451, 622105, 887131], 'label': '1728.46354.24.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336193
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.cn1.a1', '12.cq1.b1'], 'contains': ['48.bv1.a1', '48.cc1.b1', '48.cd1.a1', '72.eg1.b1', '72.ei1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6659, -1, 4814, -1, 4280, -1, 4711, -1], 'generators': [817469, 622537, 1674451, 622105, 887131], 'label': '1728.46354.24.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cp1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336194
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.cn1.a1', '12.cq1.a1'], 'contains': ['48.bw1.a1', '48.bx1.a1', '48.cd1.a1', '72.ej1.a1', '72.ek1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6622, -1, 4916, -1, 4413, -1, 4674, -1], 'generators': [46999, 622537, 1651771, 622105, 887131], 'label': '1728.46354.24.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336195
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.cn1.b1', '12.cq1.b1'], 'contains': ['48.bw1.b1', '48.bx1.a1', '48.cd1.a1', '72.ej1.b1', '72.ek1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6622, -1, 4782, -1, 4413, -1, 5056, -1], 'generators': [793511, 622537, 1651771, 622105, 887131], 'label': '1728.46354.24.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.cq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336196
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.co1.a1', '12.cs1.a1'], 'contains': ['48.bw1.a1', '48.by1.a1', '48.cb1.a1', '48.cn1.a1', '48.co1.a1', '72.el1.a1', '72.em1.a1', '72.en1.a1', '72.en1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5962, -1, 4022, -1, 4233, -1, 4102, -1], 'generators': [46999, 622105, 1634131, 887131, 622537], 'label': '1728.46354.24.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336197
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.co1.b1', '12.cs1.b1'], 'contains': ['48.bw1.b1', '48.by1.a1', '48.cb1.a1', '48.cn1.b1', '48.co1.b1', '72.el1.b1', '72.em1.b1', '72.en1.b1', '72.en1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5962, -1, 4122, -1, 4233, -1, 4144, -1], 'generators': [793511, 622105, 1634131, 887131, 622537], 'label': '1728.46354.24.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cr1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336198
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.co1.a1', '12.cs1.a1'], 'contains': ['48.bw1.a1', '48.ca1.a1', '48.ce1.a1', '72.eo1.a1', '72.ep1.a1', '72.eq1.a1', '72.eq1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5887, -1, 3795, -1, 3630, -1, 3505, -1], 'generators': [46999, 622105, 1656811, 887131, 622537], 'label': '1728.46354.24.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336199
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.co1.b1', '12.cs1.b1'], 'contains': ['48.bw1.b1', '48.ca1.a1', '48.ce1.a1', '72.eo1.b1', '72.ep1.b1', '72.eq1.b1', '72.eq1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5887, -1, 4097, -1, 3630, -1, 3480, -1], 'generators': [793511, 622105, 1656811, 887131, 622537], 'label': '1728.46354.24.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cs1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1.b1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336200
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.cn1.b1', '12.cq1.a1'], 'contains': ['48.bx1.a1', '48.bz1.a1', '48.cc1.a1', '72.er1.a1', '72.es1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6573, -1, 4743, -1, 4457, -1, 5123, -1], 'generators': [70957, 622537, 1651771, 622105, 887131], 'label': '1728.46354.24.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.ct1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336201
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.k1.a1', '12.n1.a1', '12.o1.a1', '12.ba1.a1', '12.bb1.a1', '12.bi1.a1', '12.bj1.a1', '18.c1.a1', '18.g1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3721, -1, 7095, -1, 6506, -1, 6755, -1], 'generators': [70957, 622537, 887131, 1674451, 622105, 835777, 793169], 'label': '1728.46354.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336202
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.cn1.a1', '12.cq1.b1'], 'contains': ['48.bx1.a1', '48.bz1.a1', '48.cc1.b1', '72.er1.b1', '72.es1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6573, -1, 4995, -1, 4457, -1, 4809, -1], 'generators': [817469, 622537, 1651771, 622105, 887131], 'label': '1728.46354.24.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.ct1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336203
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.co1.b1', '12.cs1.a1'], 'contains': ['48.by1.a1', '48.cc1.a1', '48.ce1.a1', '72.et1.a1', '72.eu1.a1', '72.ev1.a1', '72.ev1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6053, -1, 3829, -1, 3593, -1, 3422, -1], 'generators': [70957, 622105, 1634131, 887131, 622537], 'label': '1728.46354.24.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336204
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.co1.a1', '12.cs1.b1'], 'contains': ['48.by1.a1', '48.cc1.b1', '48.ce1.a1', '72.et1.b1', '72.eu1.b1', '72.ev1.b1', '72.ev1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6053, -1, 3697, -1, 3593, -1, 3712, -1], 'generators': [817469, 622105, 1634131, 887131, 622537], 'label': '1728.46354.24.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cu1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336205
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.co1.b1', '12.cs1.a1'], 'contains': ['48.ca1.a1', '48.cb1.a1', '48.cc1.a1', '72.ew1.a1', '72.ex1.a1', '72.ey1.a1', '72.ey1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6015, -1, 3953, -1, 3779, -1, 3454, -1], 'generators': [70957, 622105, 1656811, 887131, 622537], 'label': '1728.46354.24.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336206
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.co1.a1', '12.cs1.b1'], 'contains': ['48.ca1.a1', '48.cb1.a1', '48.cc1.b1', '72.ew1.b1', '72.ex1.b1', '72.ey1.b1', '72.ey1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6015, -1, 3742, -1, 3779, -1, 3744, -1], 'generators': [817469, 622105, 1656811, 887131, 622537], 'label': '1728.46354.24.cv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cv1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1.b1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336207
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.bl1.a1', '12.cp1.a1', '12.cp1.b1'], 'contains': ['48.e1.a1', '72.ez1.a1', '72.fa1.a1', '72.fb1.a1', '96.j1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9341, -1, 1562, -1, 1023, -1, 1271, -1], 'generators': [1674451, 70633, 1341703, 622105, 887131], 'label': '1728.46354.24.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '24.cw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336240
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.c1.a1', '16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '96.n1.a1', '96.o1.a1', '96.p1.a1', '96.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9616, -1, 987, -1, 1023, -1, 977, -1], 'generators': [46999, 622537, 622105, 1341703], 'label': '1728.46354.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.c1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336208
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.a1.a1', '12.cq1.a1', '12.cq1.b1'], 'contains': ['48.d1.a1', '48.bv1.a1', '48.bx1.a1', '72.ez1.a1', '72.fc1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8105, -1, 2887, -1, 3349, -1, 3085, -1], 'generators': [1674451, 622537, 887131, 70633, 622105], 'label': '1728.46354.24.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.cx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336209
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.b1.a1', '12.cr1.a1', '12.cr1.b1'], 'contains': ['48.f1.a1', '72.fa1.a1', '72.fc1.a1', '96.l1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8910, -1, 1247, -1, 1059, -1, 1433, -1], 'generators': [1674451, 622537, 1341703, 887131, 70633], 'label': '1728.46354.24.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.cy1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336210
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.bm1.a1'], 'contains': ['48.cg1.a1', '72.fb1.a1', '72.fc1.a1', '96.m1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8775, -1, 1178, -1, 160, -1, 886, -1], 'generators': [1674451, 622537, 766291, 887131, 70633], 'label': '1728.46354.24.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.cz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 264336211
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bn1.a1', '12.cq1.a1', '12.cs1.a1'], 'contains': ['48.d1.a1', '48.bw1.a1', '48.cc1.a1', '72.fd1.a1', '72.fe1.a1', '72.ff1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8067, -1, 2485, -1, 3176, -1, 2714, -1], 'generators': [46999, 887131, 70633, 622537, 622105], 'label': '1728.46354.24.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.da1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336212
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3456.ma', 'aut_weyl_index': 2, 'centralizer': '864.a1.a1', 'complements': ['864.e1.a1', '864.e1.b1', '864.h1.a1', '864.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.f1.a1', '6.b1.a1', '6.m1.a1', '6.p1.a1', '8.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4969, 7434, 4048, 2424, 2252, 7445, 3315, 1828], 'generators': [1674451, 887131, 70633, 835777, 793169, 622105, 622537, 1341703], 'label': '1728.46354.2.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.f1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '864.4673', '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': '864.4673'}
  • id: 264336213
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.l1.a1', '12.m1.a1', '12.n1.a1', '12.bf1.a1', '12.bg1.a1', '12.bh1.a1', '12.bk1.a1', '18.d1.a1', '18.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2360, -1, 6833, -1, 6677, -1, 6797, -1], 'generators': [70957, 622537, 887131, 1674451, 622105, 811801, 793169], 'label': '1728.46354.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336214
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.bn1.a1', '12.cq1.b1', '12.cs1.b1'], 'contains': ['48.d1.a1', '48.bw1.b1', '48.cc1.b1', '72.fd1.b1', '72.fe1.b1', '72.ff1.b1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8067, -1, 2375, -1, 3176, -1, 2780, -1], 'generators': [793511, 887131, 70633, 622537, 622105], 'label': '1728.46354.24.da1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.da1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336215
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bo1.a1', '12.cv1.a1', '12.cv1.a2'], 'contains': ['48.ch1.a1', '72.d1.a1', '72.ff1.a1', '96.q1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9873, -1, 196, -1, 664, -1, 225, -1], 'generators': [46999, 70633, 47089, 1341703, 887131], 'label': '1728.46354.24.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.db1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336216
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.bo1.a1', '12.cv1.b1', '12.cv1.b2'], 'contains': ['48.ch1.a1', '72.d1.b1', '72.ff1.b1', '96.q1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9873, -1, 230, -1, 664, -1, 332, -1], 'generators': [793511, 70633, 47089, 1341703, 887131], 'label': '1728.46354.24.db1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.db1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336217
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.bp1.a1', '12.ct1.a1', '12.ct1.b1'], 'contains': ['48.e1.a1', '72.fg1.a1', '72.fh1.a1', '96.s1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8657, -1, 925, -1, 730, -1, 637, -1], 'generators': [1634131, 622105, 1341703, 887131, 70633], 'label': '1728.46354.24.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '24.dc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336218
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.bq1.a1', '12.cu1.a1', '12.cu1.b1'], 'contains': ['48.f1.a1', '72.fg1.a1', '72.fi1.a1', '96.t1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8623, -1, 597, -1, 617, -1, 825, -1], 'generators': [1634131, 622537, 1341703, 887131, 70633], 'label': '1728.46354.24.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.dd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336219
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.br1.a1', '12.cv1.a1', '12.cv1.b1'], 'contains': ['48.ch1.a1', '72.fg1.a1', '72.fj1.a1', '96.u1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9175, -1, 162, -1, 344, -1, 264, -1], 'generators': [1634131, 47089, 1341703, 887131, 70633], 'label': '1728.46354.24.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.de1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336220
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.br1.a1', '12.cv1.a2', '12.cv1.b2'], 'contains': ['48.ch1.a1', '72.fg1.a1', '72.fj1.a2', '96.u1.a2'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9175, -1, 124, -1, 344, -1, 302, -1], 'generators': [1634131, 1197949, 1341703, 887131, 70633], 'label': '1728.46354.24.de1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.de1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.a2', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336221
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.162', 'aut_weyl_index': 32, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.e1.a1', '12.cs1.a1', '12.cs1.b1'], 'contains': ['48.d1.a1', '48.by1.a1', '48.ca1.a1', '72.fh1.a1', '72.fi1.a1', '72.fj1.a1', '72.fj1.a2'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7720, -1, 2225, -1, 3093, -1, 2468, -1], 'generators': [1634131, 622105, 887131, 70633, 622537], 'label': '1728.46354.24.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.df1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 264336222
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.bs1.a1', '12.cq1.a1', '12.cq1.b1'], 'contains': ['48.d1.a1', '48.bz1.a1', '48.cd1.a1', '72.fk1.a1', '72.fl1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8142, -1, 2851, -1, 3400, -1, 3219, -1], 'generators': [1675405, 622537, 70633, 622105, 887131], 'label': '1728.46354.24.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '24.dg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336223
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.bt1.a1', '12.cp1.a1', '12.cp1.b1'], 'contains': ['48.e1.a1', '72.fk1.a1', '72.fm1.a1', '96.x1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9553, -1, 1540, -1, 1507, -1, 1471, -1], 'generators': [1675405, 70633, 622105, 1341703, 887131], 'label': '1728.46354.24.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '24.dh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336224
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.p1.a1', '12.q1.a1', '12.t1.a1', '12.u1.a1', '12.x1.a1', '12.bb1.a1', '12.bh1.a1', '18.i1.a1', '18.k1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3004, -1, 7864, -1, 6924, -1, 7102, -1], 'generators': [46999, 622537, 887131, 1651771, 622105, 811801, 793169], 'label': '1728.46354.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336225
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '24.di1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.bu1.a1'], 'contains': ['48.cf1.a1', '72.fk1.a1', '72.fn1.a1', '96.y1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9726, -1, 1348, -1, 1738, -1, 2244, -1], 'generators': [1675405, 70633, 622105, 767155, 887131], 'label': '1728.46354.24.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bu1.a1', 'old_label': '24.di1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336226
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '24.dj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.f1.a1', '12.cr1.a1', '12.cr1.b1'], 'contains': ['48.f1.a1', '72.fl1.a1', '72.fm1.a1', '72.fn1.a1', '96.z1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9069, -1, 1211, -1, 1476, -1, 1703, -1], 'generators': [1675405, 70633, 1341703, 622537, 887131], 'label': '1728.46354.24.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.dj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336227
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.dk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.bv1.a1', '12.cs1.a1', '12.cs1.b1'], 'contains': ['48.d1.a1', '48.cb1.a1', '48.ce1.a1', '72.fo1.a1', '72.fp1.a1', '72.fq1.a1', '72.fq1.a2'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7981, -1, 2153, -1, 2980, -1, 2434, -1], 'generators': [1633789, 622105, 70633, 887131, 622537], 'label': '1728.46354.24.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.dk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 264336228
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.dl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.bw1.a1', '12.ct1.a1', '12.ct1.b1'], 'contains': ['48.e1.a1', '72.fo1.a1', '72.fr1.a1', '72.fs1.a1', '96.bc1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9032, -1, 907, -1, 374, -1, 488, -1], 'generators': [1633789, 70633, 1341703, 622105, 887131], 'label': '1728.46354.24.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '24.dl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336229
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.dm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.bx1.a1'], 'contains': ['48.cf1.a1', '72.fo1.a1', '72.ft1.a1', '72.fu1.a1', '72.fu1.a2', '96.bd1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9836, -1, 468, -1, 130, -1, 586, -1], 'generators': [1633789, 70633, 767155, 622105, 887131], 'label': '1728.46354.24.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1.a1', 'old_label': '24.dm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 264336230
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '24.dn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.by1.a1', '12.cu1.a1', '12.cu1.b1'], 'contains': ['48.f1.a1', '72.fp1.a1', '72.fr1.a1', '72.ft1.a1', '96.be1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8804, -1, 454, -1, 303, -1, 726, -1], 'generators': [1633789, 70633, 1341703, 622537, 887131], 'label': '1728.46354.24.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.dn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336231
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.bz1.a1'], 'contains': ['48.cg1.a1', '72.fp1.a1', '72.fs1.a1', '72.fu1.a1', '72.fu1.a2', '96.bf1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9507, -1, 284, -1, 10, -1, 398, -1], 'generators': [1633789, 70633, 766291, 622537, 887131], 'label': '1728.46354.24.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bz1.a1', 'old_label': '24.do1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 264336232
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.ca1.a1', '12.cv1.a1', '12.cv1.b2'], 'contains': ['48.ch1.a1', '72.fq1.a1', '72.fr1.a1', '72.fu1.a1', '96.bg1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9985, -1, 6, -1, 105, -1, 200, -1], 'generators': [1633789, 70633, 1341703, 47089, 887131], 'label': '1728.46354.24.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.dp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336233
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 48, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.ca1.a1', '12.cv1.a2', '12.cv1.b1'], 'contains': ['48.ch1.a1', '72.fq1.a2', '72.fr1.a1', '72.fu1.a2', '96.bg1.a2'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9985, -1, 37, -1, 105, -1, 179, -1], 'generators': [1633789, 70633, 1341703, 1197949, 887131], 'label': '1728.46354.24.dp1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.dp1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1.a2', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336234
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.43', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.cb1.a1'], 'contains': ['48.ci1.a1', '72.fq1.a1', '72.fs1.a1', '72.ft1.a1', '72.fu1.a2', '96.bh1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9795, -1, 255, -1, 34, -1, 378, -1], 'generators': [1633789, 70633, 766291, 47089, 887131], 'label': '1728.46354.24.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cb1.a1', 'old_label': '24.dq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 264336235
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.p1.a1', '12.r1.a1', '12.s1.a1', '12.w1.a1', '12.y1.a1', '12.bg1.a1', '12.bj1.a1', '18.j1.a1', '18.l1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1925, -1, 6642, -1, 6570, -1, 6898, -1], 'generators': [46999, 622537, 887131, 1651771, 622105, 835777, 793169], 'label': '1728.46354.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336236
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.43', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.cb1.a1'], 'contains': ['48.ci1.a1', '72.fq1.a2', '72.fs1.a1', '72.ft1.a1', '72.fu1.a1', '96.bh1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9795, -1, 269, -1, 34, -1, 358, -1], 'generators': [1633789, 70633, 190843, 1197949, 887131], 'label': '1728.46354.24.dq1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cb1.a1', 'old_label': '24.dq1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1.a2', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 264336237
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.e1.a1', '54.f1.a1', '54.g1.a1', '54.h1.a1', '54.i1.a1', '54.j1.a1', '54.k1.a1', '54.l1.a1', '54.m1.a1', '54.n1.a1', '54.o1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3814, -1, 5978, -1, 5286, -1, 5896, -1], 'generators': [46999, 1674451, 835777, 70633], 'label': '1728.46354.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336238
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1', '96.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7749, -1, 2997, -1, 1663, -1, 1658, -1], 'generators': [793169, 1341703, 622537, 622105], 'label': '1728.46354.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336239
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '16.b1.a1', '16.i1.a1', '16.i1.b1'], 'contains': ['64.a1.a1', '96.j1.a1', '96.k1.a1', '96.l1.a1', '96.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9646, -1, 1443, -1, 1259, -1, 1466, -1], 'generators': [1674451, 1341703, 622105, 622537], 'label': '1728.46354.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.b1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336241
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '16.c1.a1', '16.i1.b1', '16.j1.b1'], 'contains': ['64.a1.a1', '96.n1.b1', '96.o1.b1', '96.p1.b1', '96.q1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9616, -1, 796, -1, 1023, -1, 1051, -1], 'generators': [793511, 622537, 622105, 1341703], 'label': '1728.46354.32.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.c1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336242
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '16.d1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1', '96.u1.a2', '96.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9040, -1, 654, -1, 918, -1, 746, -1], 'generators': [1634131, 1341703, 622537, 622105], 'label': '1728.46354.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336243
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '16.e1.a1', '16.i1.a1', '16.i1.b1'], 'contains': ['64.a1.a1', '96.w1.a1', '96.x1.a1', '96.y1.a1', '96.z1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9697, -1, 1405, -1, 1707, -1, 1731, -1], 'generators': [1675405, 622105, 1341703, 622537], 'label': '1728.46354.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336244
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '216.162', 'aut_weyl_index': 32, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '16.f1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '96.bb1.a1', '96.bc1.a1', '96.bd1.a1', '96.be1.a1', '96.bf1.a1', '96.bg1.a1', '96.bg1.a2', '96.bh1.a1', '96.bh1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9272, -1, 354, -1, 551, -1, 654, -1], 'generators': [1633789, 1341703, 622537, 622105], 'label': '1728.46354.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 264336245
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': ['48.cp1.a1', '48.cr1.a2', '48.cr1.a1', '48.cp1.b1', '48.cr1.b2', '48.cr1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.bm1.a1', '18.x1.a1', '18.y1.a1', '18.z1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.k1.a1', '72.dt1.a1', '72.fc1.a1', '108.bc1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 7871, 5326, 2841, 4109, 7513, 4946, 4675], 'generators': [1674451, 622537, 793169, 887131, 70633], 'label': '1728.46354.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['72.b1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336246
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.u1.a1', '12.v1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1', '12.be1.a1', '12.bk1.a1', '18.m1.a1', '18.o1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2583, -1, 7351, -1, 6806, -1, 6841, -1], 'generators': [70957, 622537, 887131, 1651771, 622105, 811801, 793169], 'label': '1728.46354.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336247
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.bo1.a1', '18.r1.a1', '18.bf1.a1', '18.bg1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.d1.b1', '108.bd1.a1', '144.o1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7583, 993, 2118, 7383, 1384, 2070, 1301, 8466], 'generators': [46999, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.c1.a1', '12.d1.a1'], 'normal_contains': ['72.c1.a1', '72.d1.a1', '72.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336248
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '36.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '72.b1.a1', 'complements': ['48.cl1.a1', '48.cl1.b1', '48.cq1.a1', '48.cr1.a2', '48.cr1.a1', '48.cq1.b1', '48.cr1.b2', '48.cr1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.cd1.a1', '18.t1.a1', '18.bd1.a1', '18.bk1.a1'], 'contains': ['72.a1.a1', '72.w1.a1', '72.y1.a1', '108.bh1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4579, 4659, 5737, 4409, 5270, 5563, 5919, 3191], 'generators': [835777, 622105, 887131, 70633, 793169], 'label': '1728.46354.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.g1.a1', '12.h1.a1'], 'normal_contains': ['72.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336249
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.a1.a1', '18.b1.a1', '18.q1.a1'], 'contains': ['72.e1.a1', '72.g1.a1', '72.o1.a1', '72.bq1.a1', '72.cc1.a1', '72.dj1.a1', '72.ef1.a1', '72.ef1.b1', '108.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3345, -1, 8167, -1, 8641, -1, 7330, -1], 'generators': [46999, 622105, 1674451, 793169, 887131], 'label': '1728.46354.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336250
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.a1.a1', '18.c1.a1', '18.t1.a1'], 'contains': ['72.e1.a1', '72.l1.a1', '72.w1.a1', '72.bt1.a1', '72.bu1.a1', '72.cq1.a1', '72.cr1.a1', '108.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3605, -1, 7735, -1, 8598, -1, 7519, -1], 'generators': [1674451, 622105, 835777, 887131, 793169], 'label': '1728.46354.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336251
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.b1.a1', '18.d1.a1', '18.t1.a1'], 'contains': ['72.e1.a1', '72.q1.a1', '72.y1.a1', '72.bu1.a1', '72.cs1.a1', '108.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3131, -1, 7703, -1, 8043, -1, 7117, -1], 'generators': [1674451, 622105, 811801, 887131, 793169], 'label': '1728.46354.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336252
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.a1.a1', '18.d1.a1', '18.u1.a1'], 'contains': ['72.e1.a1', '72.t1.a1', '72.z1.a1', '72.bv1.a1', '72.ct1.a1', '108.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [665, -1, 7602, -1, 8332, -1, 7294, -1], 'generators': [834823, 622105, 1674451, 887131, 793169], 'label': '1728.46354.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336253
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.c1.a1', '18.d1.a1', '18.q1.a1'], 'contains': ['72.e1.a1', '72.x1.a1', '72.ba1.a1', '72.eg1.a1', '72.eg1.b1', '108.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4070, -1, 6641, -1, 6281, -1, 6038, -1], 'generators': [70957, 887131, 1674451, 793169, 622105], 'label': '1728.46354.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336254
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.b1.a1', '18.c1.a1', '18.u1.a1'], 'contains': ['72.e1.a1', '72.bb1.a1', '72.bc1.a1', '108.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3874, -1, 8187, -1, 7047, -1, 6681, -1], 'generators': [812125, 622105, 1674451, 1633643, 887131], 'label': '1728.46354.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336255
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.e1.a1', '18.f1.a1', '18.x1.a1'], 'contains': ['72.f1.a1', '72.h1.a1', '72.p1.a1', '72.by1.a1', '72.cd1.a1', '72.dk1.a1', '72.eh1.a1', '72.eh1.b1', '108.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3493, -1, 7879, -1, 7422, -1, 8257, -1], 'generators': [46999, 622537, 1674451, 793169, 887131], 'label': '1728.46354.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336256
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.e1.a1', '18.g1.a1', '18.y1.a1'], 'contains': ['72.f1.a1', '72.m1.a1', '72.bd1.a1', '72.bz1.a1', '72.ca1.a1', '72.cu1.a1', '72.cv1.a1', '108.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3923, -1, 7123, -1, 7379, -1, 8533, -1], 'generators': [1674451, 622537, 835777, 887131, 793169], 'label': '1728.46354.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336257
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.153312', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.v1.a1', '12.w1.a1', '12.x1.a1', '12.bc1.a1', '12.bd1.a1', '12.bf1.a1', '12.bi1.a1', '18.n1.a1', '18.p1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2464, -1, 7446, -1, 6996, -1, 7142, -1], 'generators': [70957, 622537, 887131, 1651771, 622105, 835777, 793169], 'label': '1728.46354.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336258
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.f1.a1', '18.h1.a1', '18.y1.a1'], 'contains': ['72.f1.a1', '72.r1.a1', '72.bf1.a1', '72.ca1.a1', '72.cw1.a1', '108.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3310, -1, 7634, -1, 6731, -1, 7823, -1], 'generators': [1674451, 622537, 811801, 887131, 793169], 'label': '1728.46354.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336259
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.e1.a1', '18.h1.a1', '18.z1.a1'], 'contains': ['72.f1.a1', '72.u1.a1', '72.bg1.a1', '72.cb1.a1', '72.cx1.a1', '108.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1973, -1, 7492, -1, 7147, -1, 8221, -1], 'generators': [834823, 622537, 1674451, 887131, 793169], 'label': '1728.46354.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336260
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.g1.a1', '18.h1.a1', '18.x1.a1'], 'contains': ['72.f1.a1', '72.be1.a1', '72.bh1.a1', '72.ei1.a1', '72.ei1.b1', '108.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4283, -1, 6426, -1, 5480, -1, 6218, -1], 'generators': [70957, 622537, 1674451, 793169, 887131], 'label': '1728.46354.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336261
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.f1.a1', '18.g1.a1', '18.z1.a1'], 'contains': ['72.f1.a1', '72.bi1.a1', '72.bj1.a1', '108.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4180, -1, 7828, -1, 6073, -1, 7224, -1], 'generators': [812125, 622537, 1674451, 1633643, 887131], 'label': '1728.46354.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336262
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.i1.a1', '18.j1.a1', '18.q1.a1'], 'contains': ['72.g1.a1', '72.j1.a1', '72.ba1.a1', '72.ej1.a1', '72.ej1.b1', '108.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2277, -1, 6283, -1, 6647, -1, 6111, -1], 'generators': [46999, 887131, 1651771, 793169, 622105], 'label': '1728.46354.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336263
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.k1.a1', '18.l1.a1', '18.x1.a1'], 'contains': ['72.h1.a1', '72.k1.a1', '72.bh1.a1', '72.ek1.a1', '72.ek1.b1', '108.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2316, -1, 6232, -1, 5576, -1, 6536, -1], 'generators': [46999, 622537, 1651771, 793169, 887131], 'label': '1728.46354.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336264
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.a1.a1', '18.i1.a1', '18.ba1.a1'], 'contains': ['72.g1.a1', '72.l1.a1', '72.t1.a1', '72.ce1.a1', '72.ch1.a1', '72.dl1.a1', '72.el1.a1', '72.el1.b1', '108.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2461, -1, 8327, -1, 8132, -1, 6968, -1], 'generators': [46999, 622105, 1634131, 793169, 887131], 'label': '1728.46354.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336265
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.e1.a1', '18.k1.a1', '18.bb1.a1'], 'contains': ['72.h1.a1', '72.m1.a1', '72.u1.a1', '72.cf1.a1', '72.ci1.a1', '72.dm1.a1', '72.em1.a1', '72.em1.b1', '108.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2525, -1, 8000, -1, 7105, -1, 7938, -1], 'generators': [46999, 622537, 1634131, 793169, 887131], 'label': '1728.46354.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336266
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.bc1.a1'], 'contains': ['72.i1.a1', '72.n1.a1', '72.v1.a1', '72.cg1.a1', '72.cj1.a1', '72.dn1.a1', '72.dn1.a2', '72.en1.a1', '72.en1.a2', '72.en1.b1', '72.en1.b2', '108.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5180, -1, 5275, -1, 5200, -1, 5190, -1], 'generators': [46999, 47089, 1634131, 793169, 887131], 'label': '1728.46354.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336267
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.b1.a1', '18.j1.a1', '18.ba1.a1'], 'contains': ['72.g1.a1', '72.q1.a1', '72.bc1.a1', '72.eo1.a1', '72.eo1.b1', '108.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3428, -1, 6259, -1, 6606, -1, 5776, -1], 'generators': [46999, 622105, 1656811, 793169, 887131], 'label': '1728.46354.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336268
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 36, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bl1.a1', '12.bt1.a1', '12.cp1.a1', '12.cp1.b1', '18.q1.a1', '18.r1.a1', '24.y1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7750, -1, 3282, -1, 2111, -1, 2130, -1], 'generators': [46999, 887131, 1341703, 1674451, 70633, 793169, 622105], 'label': '1728.46354.6.l1.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.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336269
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.f1.a1', '18.l1.a1', '18.bb1.a1'], 'contains': ['72.h1.a1', '72.r1.a1', '72.bj1.a1', '72.ep1.a1', '72.ep1.b1', '108.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3654, -1, 6193, -1, 5531, -1, 6175, -1], 'generators': [46999, 622537, 1656811, 793169, 887131], 'label': '1728.46354.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336270
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.bc1.a1'], 'contains': ['72.i1.a1', '72.s1.a1', '72.bl1.a1', '72.eq1.a1', '72.eq1.a2', '72.eq1.b1', '72.eq1.b2', '108.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5675, -1, 4140, -1, 4844, -1, 4439, -1], 'generators': [46999, 47089, 1656811, 793169, 887131], 'label': '1728.46354.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336271
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '18.a1.a1', '18.j1.a1', '18.bd1.a1'], 'contains': ['72.g1.a1', '72.w1.a1', '72.z1.a1', '72.ck1.a1', '72.cl1.a1', '108.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [460, -1, 6572, -1, 8380, -1, 7406, -1], 'generators': [46999, 622105, 835777, 887131, 793169], 'label': '1728.46354.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336272
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '18.b1.a1', '18.i1.a1', '18.bd1.a1'], 'contains': ['72.g1.a1', '72.y1.a1', '72.bb1.a1', '108.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2486, -1, 8347, -1, 7643, -1, 6819, -1], 'generators': [46999, 622105, 811801, 793169, 887131], 'label': '1728.46354.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336273
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '18.e1.a1', '18.l1.a1', '18.be1.a1'], 'contains': ['72.h1.a1', '72.bd1.a1', '72.bg1.a1', '72.cm1.a1', '72.cn1.a1', '108.j1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1267, -1, 6841, -1, 7194, -1, 8378, -1], 'generators': [46999, 793169, 835777, 887131, 622537], 'label': '1728.46354.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336274
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '18.f1.a1', '18.k1.a1', '18.be1.a1'], 'contains': ['72.h1.a1', '72.bf1.a1', '72.bi1.a1', '108.k1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2222, -1, 8042, -1, 6419, -1, 7674, -1], 'generators': [46999, 887131, 811801, 622537, 793169], 'label': '1728.46354.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336275
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '18.i1.a1', '18.m1.a1', '18.t1.a1'], 'contains': ['72.j1.a1', '72.l1.a1', '72.y1.a1', '72.cq1.a1', '72.cs1.a1', '108.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2046, -1, 8274, -1, 7677, -1, 7005, -1], 'generators': [1651771, 622105, 811801, 887131, 793169], 'label': '1728.46354.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336276
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.m1.a1', '18.n1.a1', '18.q1.a1'], 'contains': ['72.j1.a1', '72.o1.a1', '72.x1.a1', '72.er1.a1', '72.er1.b1', '108.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1647, -1, 7424, -1, 6865, -1, 6141, -1], 'generators': [70957, 887131, 1651771, 793169, 622105], 'label': '1728.46354.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336277
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.j1.a1', '18.n1.a1', '18.t1.a1'], 'contains': ['72.j1.a1', '72.q1.a1', '72.w1.a1', '72.cr1.a1', '72.cs1.a1', '108.n1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [713, -1, 6535, -1, 7817, -1, 7042, -1], 'generators': [1651771, 622105, 835777, 887131, 793169], 'label': '1728.46354.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336278
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.i1.a1', '18.n1.a1', '18.u1.a1'], 'contains': ['72.j1.a1', '72.t1.a1', '72.bb1.a1', '72.do1.a1', '108.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1601, -1, 8301, -1, 7608, -1, 6790, -1], 'generators': [812125, 622105, 1651771, 887131, 1633643], 'label': '1728.46354.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336279
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.h1.a1', '12.bl1.a1', '12.bp1.a1', '18.s1.a1', '18.t1.a1', '24.z1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4962, -1, 4272, -1, 2274, -1, 3267, -1], 'generators': [1674451, 70633, 887131, 835777, 622105, 1341703, 793169], 'label': '1728.46354.6.m1.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.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336280
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.j1.a1', '18.m1.a1', '18.u1.a1'], 'contains': ['72.j1.a1', '72.z1.a1', '72.bc1.a1', '108.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1316, -1, 6369, -1, 6920, -1, 6486, -1], 'generators': [834823, 622105, 1651771, 793169, 887131], 'label': '1728.46354.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336281
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '18.k1.a1', '18.o1.a1', '18.y1.a1'], 'contains': ['72.k1.a1', '72.m1.a1', '72.bf1.a1', '72.cu1.a1', '72.cw1.a1', '108.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2975, -1, 7762, -1, 6687, -1, 7786, -1], 'generators': [1651771, 622537, 811801, 887131, 793169], 'label': '1728.46354.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336282
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.o1.a1', '18.p1.a1', '18.x1.a1'], 'contains': ['72.k1.a1', '72.p1.a1', '72.be1.a1', '72.es1.a1', '72.es1.b1', '108.m1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2603, -1, 6696, -1, 5774, -1, 6573, -1], 'generators': [70957, 622537, 1651771, 793169, 887131], 'label': '1728.46354.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336283
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.l1.a1', '18.p1.a1', '18.y1.a1'], 'contains': ['72.k1.a1', '72.r1.a1', '72.bd1.a1', '72.cv1.a1', '72.cw1.a1', '108.n1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1940, -1, 6390, -1, 6328, -1, 7749, -1], 'generators': [1651771, 622537, 835777, 887131, 793169], 'label': '1728.46354.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336284
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.k1.a1', '18.p1.a1', '18.z1.a1'], 'contains': ['72.k1.a1', '72.u1.a1', '72.bi1.a1', '72.dp1.a1', '108.o1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2414, -1, 7974, -1, 6372, -1, 7635, -1], 'generators': [812125, 622537, 1651771, 887131, 1633643], 'label': '1728.46354.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336285
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.l1.a1', '18.o1.a1', '18.z1.a1'], 'contains': ['72.k1.a1', '72.bg1.a1', '72.bj1.a1', '108.p1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1826, -1, 6322, -1, 5808, -1, 6941, -1], 'generators': [834823, 622537, 1651771, 793169, 887131], 'label': '1728.46354.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336286
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.a1.a1', '18.m1.a1', '18.bi1.a1'], 'contains': ['72.l1.a1', '72.o1.a1', '72.z1.a1', '72.cz1.a1', '72.db1.a1', '108.q1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1349, -1, 7788, -1, 8553, -1, 7366, -1], 'generators': [834823, 622105, 1634131, 887131, 793169], 'label': '1728.46354.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336287
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.e1.a1', '18.o1.a1', '18.bj1.a1'], 'contains': ['72.m1.a1', '72.p1.a1', '72.bg1.a1', '72.da1.a1', '72.de1.a1', '108.q1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2116, -1, 7532, -1, 7335, -1, 8339, -1], 'generators': [834823, 622537, 1634131, 887131, 793169], 'label': '1728.46354.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336288
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.c1.a1', '18.m1.a1', '18.ba1.a1'], 'contains': ['72.l1.a1', '72.x1.a1', '72.bc1.a1', '72.et1.a1', '72.et1.b1', '108.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4142, -1, 7384, -1, 6185, -1, 5602, -1], 'generators': [70957, 622105, 1634131, 793169, 887131], 'label': '1728.46354.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336289
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.c1.a1', '18.i1.a1', '18.bi1.a1'], 'contains': ['72.l1.a1', '72.ba1.a1', '72.bb1.a1', '108.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4097, -1, 8214, -1, 6896, -1, 6622, -1], 'generators': [812125, 622105, 1634131, 1633643, 887131], 'label': '1728.46354.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bo1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336290
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.i1.a1', '12.bl1.a1', '12.bw1.a1', '18.u1.a1', '18.v1.a1', '18.w1.a1', '24.ba1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6846, -1, 3571, -1, 1883, -1, 2174, -1], 'generators': [834823, 887131, 622105, 1674451, 70633, 793169, 1341703], 'label': '1728.46354.6.n1.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.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336291
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.g1.a1', '18.o1.a1', '18.bb1.a1'], 'contains': ['72.m1.a1', '72.be1.a1', '72.bj1.a1', '72.eu1.a1', '72.eu1.b1', '108.r1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4346, -1, 6610, -1, 5380, -1, 5839, -1], 'generators': [70957, 622537, 1634131, 793169, 887131], 'label': '1728.46354.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336292
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.g1.a1', '18.k1.a1', '18.bj1.a1'], 'contains': ['72.m1.a1', '72.bh1.a1', '72.bi1.a1', '108.s1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4221, -1, 7676, -1, 5979, -1, 7166, -1], 'generators': [812125, 622537, 1634131, 1633643, 887131], 'label': '1728.46354.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336293
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.bc1.a1'], 'contains': ['72.n1.a1', '72.bk1.a1', '72.bl1.a1', '72.ev1.a1', '72.ev1.a2', '72.ev1.b1', '72.ev1.b2', '108.r1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5896, -1, 4966, -1, 4670, -1, 4360, -1], 'generators': [70957, 47089, 1634131, 793169, 887131], 'label': '1728.46354.36.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.br1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336294
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.b1.a1', '18.n1.a1', '18.bi1.a1'], 'contains': ['72.o1.a1', '72.q1.a1', '72.bb1.a1', '72.dq1.a1', '108.t1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2658, -1, 8141, -1, 7999, -1, 7079, -1], 'generators': [812125, 622105, 1656811, 887131, 1633643], 'label': '1728.46354.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336295
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.a1.a1', '18.n1.a1', '18.bk1.a1'], 'contains': ['72.o1.a1', '72.t1.a1', '72.w1.a1', '72.dc1.a1', '72.dd1.a1', '108.u1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [747, -1, 7905, -1, 8458, -1, 7446, -1], 'generators': [1675405, 622105, 835777, 887131, 793169], 'label': '1728.46354.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bt1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336296
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.b1.a1', '18.m1.a1', '18.bk1.a1'], 'contains': ['72.o1.a1', '72.y1.a1', '72.bc1.a1', '108.v1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2882, -1, 8020, -1, 7071, -1, 6761, -1], 'generators': [1675405, 622105, 811801, 1633643, 887131], 'label': '1728.46354.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336297
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.f1.a1', '18.p1.a1', '18.bj1.a1'], 'contains': ['72.p1.a1', '72.r1.a1', '72.bi1.a1', '72.dr1.a1', '108.t1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3202, -1, 7854, -1, 6775, -1, 8020, -1], 'generators': [812125, 622537, 1656811, 887131, 1633643], 'label': '1728.46354.36.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336298
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.e1.a1', '18.p1.a1', '18.bl1.a1'], 'contains': ['72.p1.a1', '72.u1.a1', '72.bd1.a1', '72.df1.a1', '72.dg1.a1', '108.u1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2005, -1, 7558, -1, 7291, -1, 8497, -1], 'generators': [1675405, 622537, 835777, 887131, 793169], 'label': '1728.46354.36.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336299
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.f1.a1', '18.o1.a1', '18.bl1.a1'], 'contains': ['72.p1.a1', '72.bf1.a1', '72.bj1.a1', '108.v1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3378, -1, 7655, -1, 6097, -1, 7265, -1], 'generators': [1675405, 622537, 811801, 1633643, 887131], 'label': '1728.46354.36.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336300
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.d1.a1', '18.n1.a1', '18.ba1.a1'], 'contains': ['72.q1.a1', '72.t1.a1', '72.x1.a1', '72.ew1.a1', '72.ew1.b1', '108.w1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1443, -1, 6722, -1, 6561, -1, 5739, -1], 'generators': [70957, 622105, 1656811, 793169, 887131], 'label': '1728.46354.36.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.by1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336301
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.j1.a1', '12.n1.a1', '12.p1.a1', '12.v1.a1', '12.bn1.a1', '12.bs1.a1', '12.cn1.a1', '12.cn1.b1', '12.cq1.a1', '12.cq1.b1', '18.q1.a1', '18.x1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5538, -1, 5226, -1, 4778, -1, 5163, -1], 'generators': [46999, 887131, 622105, 1674451, 622537, 793169, 70633], 'label': '1728.46354.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336302
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.h1.a1', '18.p1.a1', '18.bb1.a1'], 'contains': ['72.r1.a1', '72.u1.a1', '72.be1.a1', '72.ex1.a1', '72.ex1.b1', '108.w1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2374, -1, 7354, -1, 5430, -1, 6077, -1], 'generators': [70957, 622537, 1656811, 793169, 887131], 'label': '1728.46354.36.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.bz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336303
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.bc1.a1'], 'contains': ['72.s1.a1', '72.v1.a1', '72.bk1.a1', '72.ey1.a1', '72.ey1.a2', '72.ey1.b1', '72.ey1.b2', '108.w1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4690, -1, 4517, -1, 4720, -1, 4402, -1], 'generators': [70957, 47089, 1656811, 793169, 887131], 'label': '1728.46354.36.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.ca1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336304
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.d1.a1', '18.j1.a1', '18.bi1.a1'], 'contains': ['72.q1.a1', '72.z1.a1', '72.ba1.a1', '108.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [894, -1, 6481, -1, 6834, -1, 6507, -1], 'generators': [834823, 622105, 1656811, 793169, 887131], 'label': '1728.46354.36.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336305
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.h1.a1', '18.l1.a1', '18.bj1.a1'], 'contains': ['72.r1.a1', '72.bg1.a1', '72.bh1.a1', '108.x1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1808, -1, 6307, -1, 5740, -1, 7146, -1], 'generators': [834823, 622537, 1656811, 793169, 887131], 'label': '1728.46354.36.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.cc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336306
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.d1.a1', '18.i1.a1', '18.bk1.a1'], 'contains': ['72.t1.a1', '72.y1.a1', '72.ba1.a1', '108.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2172, -1, 7161, -1, 6977, -1, 6701, -1], 'generators': [1651447, 622105, 811801, 1633643, 887131], 'label': '1728.46354.36.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336307
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.h1.a1', '18.k1.a1', '18.bl1.a1'], 'contains': ['72.u1.a1', '72.bf1.a1', '72.bh1.a1', '108.y1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2349, -1, 7033, -1, 5908, -1, 7244, -1], 'generators': [1651447, 622537, 811801, 1633643, 887131], 'label': '1728.46354.36.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.ce1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336308
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.c1.a1', '18.n1.a1', '18.bd1.a1'], 'contains': ['72.w1.a1', '72.x1.a1', '72.bb1.a1', '108.z1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1899, -1, 7454, -1, 7012, -1, 6651, -1], 'generators': [70957, 622105, 835777, 793169, 887131], 'label': '1728.46354.36.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336309
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.c1.a1', '18.j1.a1', '18.bk1.a1'], 'contains': ['72.w1.a1', '72.ba1.a1', '72.bc1.a1', '108.ba1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4042, -1, 6354, -1, 6809, -1, 6401, -1], 'generators': [1651447, 622105, 835777, 793169, 887131], 'label': '1728.46354.36.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336310
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.d1.a1', '18.m1.a1', '18.bd1.a1'], 'contains': ['72.x1.a1', '72.y1.a1', '72.z1.a1', '108.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1508, -1, 7050, -1, 6949, -1, 6378, -1], 'generators': [70957, 622105, 811801, 793169, 887131], 'label': '1728.46354.36.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.ch1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336311
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.g1.a1', '18.p1.a1', '18.be1.a1'], 'contains': ['72.bd1.a1', '72.be1.a1', '72.bi1.a1', '108.z1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1852, -1, 6999, -1, 6038, -1, 7195, -1], 'generators': [70957, 887131, 835777, 622537, 793169], 'label': '1728.46354.36.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.ci1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336312
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '12.bq1.a1', '12.ce1.a1', '18.s1.a1', '18.y1.a1', '24.bd1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4926, -1, 4133, -1, 2229, -1, 3304, -1], 'generators': [1674451, 70633, 887131, 835777, 622537, 1341703, 793169], 'label': '1728.46354.6.p1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336313
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.g1.a1', '18.l1.a1', '18.bl1.a1'], 'contains': ['72.bd1.a1', '72.bh1.a1', '72.bj1.a1', '108.ba1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4249, -1, 6081, -1, 5614, -1, 6880, -1], 'generators': [1651447, 622537, 835777, 793169, 887131], 'label': '1728.46354.36.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.cj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336314
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.h1.a1', '18.o1.a1', '18.be1.a1'], 'contains': ['72.be1.a1', '72.bf1.a1', '72.bg1.a1', '108.bb1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1774, -1, 6754, -1, 5873, -1, 6848, -1], 'generators': [70957, 887131, 811801, 622537, 793169], 'label': '1728.46354.36.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.ck1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336315
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bl1.a1', '18.q1.a1', '18.t1.a1', '18.u1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.j1.a1', '72.ds1.a1', '72.ez1.a1', '108.bc1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5072, -1, 5353, -1, 4369, -1, 4911, -1], 'generators': [1674451, 622105, 793169, 887131, 70633], 'label': '1728.46354.36.cl1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.cl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336316
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.bl1.a1', '18.r1.a1', '18.s1.a1', '18.v1.a1'], 'contains': ['72.c1.a1', '72.fa1.a1', '108.bc1.a1', '144.j1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6984, -1, 3333, -1, 1854, -1, 2049, -1], 'generators': [1674451, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.cm1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.cm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336317
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '12.bm1.a1', '18.w1.a1'], 'contains': ['72.bn1.a1', '72.fb1.a1', '108.bc1.a1', '144.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8056, -1, 2448, -1, 542, -1, 1026, -1], 'generators': [1674451, 70633, 793169, 766291, 887131], 'label': '1728.46354.36.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.cn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336318
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.bn1.a1', '18.q1.a1', '18.ba1.a1', '18.bd1.a1'], 'contains': ['72.a1.a1', '72.g1.a1', '72.x1.a1', '72.du1.a1', '72.du1.b1', '72.fd1.a1', '72.fd1.b1', '108.bd1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6121, -1, 4419, -1, 4190, -1, 4216, -1], 'generators': [46999, 887131, 793169, 70633, 622105], 'label': '1728.46354.36.co1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.co1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336319
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.bn1.a1', '18.x1.a1', '18.bb1.a1', '18.be1.a1'], 'contains': ['72.b1.a1', '72.h1.a1', '72.be1.a1', '72.dv1.a1', '72.dv1.b1', '72.fe1.a1', '72.fe1.b1', '108.bd1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6093, -1, 4632, -1, 3935, -1, 4605, -1], 'generators': [46999, 887131, 793169, 70633, 622537], 'label': '1728.46354.36.cp1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336320
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.bo1.a1', '18.bc1.a1'], 'contains': ['72.i1.a1', '72.bk1.a1', '72.bm1.a1', '72.dw1.a1', '72.dw1.b1', '72.ff1.a1', '72.ff1.b1', '108.bd1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7472, -1, 2170, -1, 3302, -1, 2843, -1], 'generators': [46999, 887131, 793169, 70633, 47089], 'label': '1728.46354.36.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '36.cq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336321
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '12.bq1.a1', '12.br1.a1', '18.s1.a1', '18.bf1.a1', '18.bh1.a1'], 'contains': ['72.c1.a1', '72.fg1.a1', '108.be1.a1', '144.r1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7250, -1, 2988, -1, 1262, -1, 1543, -1], 'generators': [1634131, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.cr1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.cr1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336322
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.bp1.a1', '18.t1.a1', '18.ba1.a1', '18.bi1.a1'], 'contains': ['72.a1.a1', '72.l1.a1', '72.q1.a1', '72.dx1.a1', '72.fh1.a1', '108.be1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5134, -1, 5466, -1, 4150, -1, 4284, -1], 'generators': [1634131, 622105, 793169, 887131, 70633], 'label': '1728.46354.36.cs1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.cs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336323
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3456.ma', 'aut_weyl_index': 2, 'centralizer': '864.a1.a1', 'complements': ['864.e1.a1', '864.e1.b1', '864.g1.a1', '864.i1.a1', '864.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1', '6.n1.a1', '6.q1.a1', '6.r1.a1', '6.s1.a1', '8.e1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6846, 3528, 3614, 5228, 1912, 3778, 2325, 4572], 'generators': [834823, 622537, 622105, 1674451, 1341703, 70633, 887131, 793169], 'label': '1728.46354.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '864.4673', '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': '864.4673'}
  • id: 264336324
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.m1.a1', '12.o1.a1', '12.x1.a1', '12.y1.a1', '12.bv1.a1', '12.cc1.a1', '18.u1.a1', '18.z1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4796, -1, 5783, -1, 5466, -1, 6118, -1], 'generators': [834823, 622537, 887131, 1674451, 622105, 70633, 793169], 'label': '1728.46354.6.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336325
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.bq1.a1', '18.y1.a1', '18.bb1.a1', '18.bj1.a1'], 'contains': ['72.b1.a1', '72.m1.a1', '72.r1.a1', '72.dy1.a1', '72.fi1.a1', '108.be1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5103, -1, 5442, -1, 3895, -1, 4638, -1], 'generators': [1634131, 622537, 793169, 887131, 70633], 'label': '1728.46354.36.ct1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.ct1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336326
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.br1.a1', '18.bc1.a1'], 'contains': ['72.n1.a1', '72.s1.a1', '72.bm1.a1', '72.dz1.a1', '72.dz1.a2', '72.fj1.a1', '72.fj1.a2', '108.be1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7443, -1, 2194, -1, 3263, -1, 2998, -1], 'generators': [1634131, 47089, 793169, 887131, 70633], 'label': '1728.46354.36.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '36.cu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336327
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '18.q1.a1', '18.bi1.a1', '18.bk1.a1'], 'contains': ['72.a1.a1', '72.o1.a1', '72.ba1.a1', '72.ea1.a1', '72.fk1.a1', '108.bf1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6178, -1, 5299, -1, 4803, -1, 5300, -1], 'generators': [1675405, 887131, 793169, 70633, 622105], 'label': '1728.46354.36.cv1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336328
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bs1.a1', '18.x1.a1', '18.bj1.a1', '18.bl1.a1'], 'contains': ['72.b1.a1', '72.p1.a1', '72.bh1.a1', '72.eb1.a1', '72.fl1.a1', '108.bf1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5292, -1, 5397, -1, 4620, -1, 5560, -1], 'generators': [1675405, 622537, 793169, 70633, 887131], 'label': '1728.46354.36.cw1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336329
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bt1.a1', '18.r1.a1', '18.bh1.a1', '18.bm1.a1'], 'contains': ['72.c1.a1', '72.fm1.a1', '108.bf1.a1', '144.x1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7133, -1, 3471, -1, 2461, -1, 3542, -1], 'generators': [1675405, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.cx1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.cx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336330
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bu1.a1', '18.bn1.a1'], 'contains': ['72.bo1.a1', '72.fn1.a1', '108.bf1.a1', '144.y1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8131, -1, 2496, -1, 2075, -1, 5157, -1], 'generators': [1675405, 70633, 793169, 767155, 887131], 'label': '1728.46354.36.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1.a1', 'old_label': '36.cy1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336331
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '12.bw1.a1', '12.bx1.a1', '18.u1.a1', '18.ba1.a1', '18.bk1.a1'], 'contains': ['72.a1.a1', '72.t1.a1', '72.bc1.a1', '72.ec1.a1', '72.fo1.a1', '108.bg1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5731, -1, 5212, -1, 3741, -1, 3984, -1], 'generators': [1633789, 622105, 793169, 70633, 887131], 'label': '1728.46354.36.cz1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336332
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '12.by1.a1', '12.bz1.a1', '18.z1.a1', '18.bb1.a1', '18.bl1.a1'], 'contains': ['72.b1.a1', '72.u1.a1', '72.bj1.a1', '72.ed1.a1', '72.fp1.a1', '108.bg1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5446, -1, 4657, -1, 3548, -1, 4063, -1], 'generators': [1633789, 622537, 793169, 70633, 887131], 'label': '1728.46354.36.da1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.da1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336333
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '12.ca1.a1', '12.cb1.a1', '18.bc1.a1'], 'contains': ['72.v1.a1', '72.bl1.a1', '72.bm1.a1', '72.ee1.a1', '72.ee1.a2', '72.fq1.a1', '72.fq1.a2', '108.bg1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8971, -1, 1918, -1, 3219, -1, 2507, -1], 'generators': [1633789, 47089, 793169, 70633, 887131], 'label': '1728.46354.36.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.db1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336334
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '12.by1.a1', '12.ca1.a1', '18.v1.a1', '18.bf1.a1', '18.bm1.a1'], 'contains': ['72.c1.a1', '72.fr1.a1', '108.bg1.a1', '144.bf1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7206, -1, 2585, -1, 1116, -1, 1232, -1], 'generators': [1633789, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.dc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.dc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336335
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '12.by1.a1', '12.cf1.a1', '18.v1.a1', '18.z1.a1', '24.bg1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5692, -1, 3525, -1, 1940, -1, 2348, -1], 'generators': [834823, 887131, 622537, 1674451, 70633, 793169, 1341703], 'label': '1728.46354.6.r1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336336
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '12.bz1.a1', '12.cb1.a1', '18.w1.a1'], 'contains': ['72.bn1.a1', '72.fs1.a1', '108.bg1.a1', '144.bg1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7998, -1, 1245, -1, 196, -1, 675, -1], 'generators': [1633789, 70633, 793169, 766291, 887131], 'label': '1728.46354.36.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.w1.a1', 'old_label': '36.dd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336337
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '12.by1.a1', '12.cb1.a1', '18.bn1.a1'], 'contains': ['72.bo1.a1', '72.ft1.a1', '108.bg1.a1', '144.bh1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9188, -1, 1813, -1, 914, -1, 1960, -1], 'generators': [1633789, 70633, 793169, 767155, 887131], 'label': '1728.46354.36.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1.a1', 'old_label': '36.de1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336338
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '12.bz1.a1', '12.ca1.a1', '12.cb1.a1'], 'contains': ['72.bp1.a1', '72.fu1.a1', '72.fu1.a2', '108.bg1.a1', '144.bi1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9419, -1, 889, -1, 75, -1, 561, -1], 'generators': [1633789, 70633, 793169, 1342135, 887131], 'label': '1728.46354.36.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.df1.a1', 'old_label': '36.df1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336339
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.dg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.cc1.a1', '18.u1.a1', '18.bd1.a1', '18.bi1.a1'], 'contains': ['72.a1.a1', '72.z1.a1', '72.bb1.a1', '108.bi1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4870, -1, 6106, -1, 5233, -1, 5805, -1], 'generators': [834823, 622105, 70633, 793169, 887131], 'label': '1728.46354.36.dg1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.dg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336340
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '36.dh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.ce1.a1', '18.y1.a1', '18.be1.a1', '18.bl1.a1'], 'contains': ['72.b1.a1', '72.bd1.a1', '72.bf1.a1', '108.bh1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4409, -1, 5788, -1, 5154, -1, 5960, -1], 'generators': [835777, 793169, 887131, 70633, 622537], 'label': '1728.46354.36.dh1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.dh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336341
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.di1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1.a1', '12.cf1.a1', '12.cg1.a1', '18.z1.a1', '18.be1.a1', '18.bj1.a1'], 'contains': ['72.b1.a1', '72.bg1.a1', '72.bi1.a1', '108.bi1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4921, -1, 5854, -1, 4978, -1, 5375, -1], 'generators': [834823, 887131, 70633, 622537, 793169], 'label': '1728.46354.36.di1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.di1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.di1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336342
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.dj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.ce1.a1', '18.s1.a1', '18.bg1.a1', '18.bm1.a1'], 'contains': ['72.c1.a1', '108.bh1.a1', '144.bo1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4802, -1, 4313, -1, 2647, -1, 3284, -1], 'generators': [835777, 70633, 1341703, 793169, 887131], 'label': '1728.46354.36.dj1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.dj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336343
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '36.dk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.cf1.a1', '18.v1.a1', '18.bg1.a1', '18.bh1.a1'], 'contains': ['72.c1.a1', '108.bi1.a1', '144.bp1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5559, -1, 5572, -1, 2728, -1, 2571, -1], 'generators': [834823, 70633, 793169, 1341703, 887131], 'label': '1728.46354.36.dk1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.dk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336344
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.cg1.a1', '18.w1.a1'], 'contains': ['72.bn1.a1', '108.bi1.a1', '144.bq1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7274, -1, 3677, -1, 2035, -1, 1326, -1], 'generators': [834823, 70633, 793169, 766291, 887131], 'label': '1728.46354.36.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '36.dl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336345
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '12.ce1.a1', '18.bn1.a1'], 'contains': ['72.bo1.a1', '108.bh1.a1', '144.br1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6947, -1, 3090, -1, 2283, -1, 5269, -1], 'generators': [835777, 70633, 767155, 793169, 887131], 'label': '1728.46354.36.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '36.dm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336346
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['12.bm1.a1', '12.bz1.a1', '12.cg1.a1', '18.w1.a1', '18.z1.a1', '24.bh1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7480, -1, 2418, -1, 1106, -1, 1577, -1], 'generators': [834823, 887131, 622537, 1674451, 70633, 793169, 766291], 'label': '1728.46354.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '6.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336347
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '12.ci1.a1', '18.a1.a1'], 'contains': ['72.bq1.a1', '72.bt1.a1', '72.bv1.a1', '72.ce1.a1', '72.ck1.a1', '72.cz1.a1', '72.dc1.a1', '108.bj1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4458, -1, 7084, -1, 8745, -1, 7556, -1], 'generators': [46999, 622105, 1674451, 835777, 793169], 'label': '1728.46354.36.dn1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.dn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336348
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.a1.a1'], 'contains': ['72.bq1.a1', '72.bu1.a1', '72.bv1.a1', '72.ch1.a1', '72.cl1.a1', '72.db1.a1', '72.dd1.a1', '108.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [272, -1, 9195, -1, 9500, -1, 8633, -1], 'generators': [46999, 622105, 1674451, 1674955, 793169], 'label': '1728.46354.36.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.do1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336349
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.dp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '12.ch1.a1', '12.ck1.a1'], 'contains': ['72.br1.a1', '72.bs1.a1', '72.bw1.a1', '72.co1.a1', '72.cp1.a1', '72.cy1.a1', '72.dh1.a1', '108.bj1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5255, -1, 5249, -1, 2550, -1, 3388, -1], 'generators': [46999, 1341703, 1674451, 835777, 793169], 'label': '1728.46354.36.dp1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '36.dp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336350
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '12.ck1.a1', '18.e1.a1'], 'contains': ['72.by1.a1', '72.bz1.a1', '72.cb1.a1', '72.cf1.a1', '72.cm1.a1', '72.da1.a1', '72.df1.a1', '108.bj1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4491, -1, 6967, -1, 7507, -1, 8775, -1], 'generators': [46999, 622537, 1674451, 835777, 793169], 'label': '1728.46354.36.dq1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.dq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336351
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.e1.a1'], 'contains': ['72.by1.a1', '72.ca1.a1', '72.cb1.a1', '72.ci1.a1', '72.cn1.a1', '72.de1.a1', '72.dg1.a1', '108.bk1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [980, -1, 9001, -1, 8909, -1, 9317, -1], 'generators': [46999, 622537, 1674451, 1674955, 793169], 'label': '1728.46354.36.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.dr1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336352
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ds1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1.a1', '18.a1.a1'], 'contains': ['72.cc1.a1', '72.ce1.a1', '72.cl1.a1', '72.cq1.a1', '72.ct1.a1', '72.cz1.a1', '72.dd1.a1', '108.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [239, -1, 9246, -1, 9380, -1, 8596, -1], 'generators': [46999, 622105, 835273, 1674955, 793169], 'label': '1728.46354.36.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.ds1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336353
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cm1.a1', '18.a1.a1'], 'contains': ['72.cc1.a1', '72.ch1.a1', '72.ck1.a1', '72.cr1.a1', '72.ct1.a1', '72.db1.a1', '72.dc1.a1', '108.bm1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [15, -1, 9169, -1, 9455, -1, 8670, -1], 'generators': [46999, 622105, 835273, 835777, 793169], 'label': '1728.46354.36.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.dt1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336354
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.du1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1.a1', '18.e1.a1'], 'contains': ['72.cd1.a1', '72.cf1.a1', '72.cn1.a1', '72.cu1.a1', '72.cx1.a1', '72.da1.a1', '72.dg1.a1', '108.bl1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [625, -1, 9118, -1, 8790, -1, 9211, -1], 'generators': [46999, 622537, 835273, 1674955, 793169], 'label': '1728.46354.36.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.du1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.du1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336355
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cm1.a1', '18.e1.a1'], 'contains': ['72.cd1.a1', '72.ci1.a1', '72.cm1.a1', '72.cv1.a1', '72.cx1.a1', '72.de1.a1', '72.df1.a1', '108.bm1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [335, -1, 8773, -1, 8953, -1, 9265, -1], 'generators': [46999, 622537, 835273, 835777, 793169], 'label': '1728.46354.36.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.dv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336356
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1.a1', '18.q1.a1'], 'contains': ['72.ds1.a1', '72.du1.a1', '72.ea1.a1', '72.ef1.a1', '72.eg1.b1', '72.ej1.a1', '72.er1.b1', '108.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6537, -1, 4736, -1, 4579, -1, 4745, -1], 'generators': [46999, 887131, 1674451, 817145, 622105], 'label': '1728.46354.36.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '36.dw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336357
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.q1.a1', '12.r1.a1', '12.ba1.a1', '12.bf1.a1', '12.bn1.a1', '12.bv1.a1', '12.co1.a1', '12.co1.b1', '12.cs1.a1', '12.cs1.b1', '18.ba1.a1', '18.bb1.a1', '18.bc1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5493, -1, 5146, -1, 4043, -1, 4107, -1], 'generators': [46999, 622537, 887131, 1634131, 622105, 793169, 70633], 'label': '1728.46354.6.t1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336358
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1.b1', '18.q1.a1'], 'contains': ['72.ds1.a1', '72.du1.b1', '72.ea1.a1', '72.ef1.b1', '72.eg1.a1', '72.ej1.b1', '72.er1.a1', '108.bn1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6537, -1, 4699, -1, 4579, -1, 4843, -1], 'generators': [70957, 887131, 1674451, 817145, 622105], 'label': '1728.46354.36.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '36.dw1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336359
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1.a1', '18.x1.a1'], 'contains': ['72.dt1.a1', '72.dv1.a1', '72.eb1.a1', '72.eh1.a1', '72.ei1.b1', '72.ek1.a1', '72.es1.b1', '108.bn1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6564, -1, 5170, -1, 4497, -1, 4775, -1], 'generators': [46999, 622537, 1674451, 817145, 887131], 'label': '1728.46354.36.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '36.dx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336360
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.dx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1.b1', '18.x1.a1'], 'contains': ['72.dt1.a1', '72.dv1.b1', '72.eb1.a1', '72.eh1.b1', '72.ei1.a1', '72.ek1.b1', '72.es1.a1', '108.bn1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6564, -1, 5097, -1, 4497, -1, 5090, -1], 'generators': [70957, 622537, 1674451, 817145, 887131], 'label': '1728.46354.36.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '36.dx1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dx1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336361
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.a1', '18.ba1.a1'], 'contains': ['72.du1.a1', '72.dx1.a1', '72.ec1.a1', '72.el1.a1', '72.eo1.a1', '72.et1.b1', '72.ew1.b1', '108.bo1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5791, -1, 3782, -1, 3814, -1, 3838, -1], 'generators': [46999, 622105, 1634131, 817145, 887131], 'label': '1728.46354.36.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '36.dy1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336362
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.b1', '18.ba1.a1'], 'contains': ['72.du1.b1', '72.dx1.a1', '72.ec1.a1', '72.el1.b1', '72.eo1.b1', '72.et1.a1', '72.ew1.a1', '108.bo1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5791, -1, 3840, -1, 3814, -1, 3808, -1], 'generators': [70957, 622105, 1634131, 817145, 887131], 'label': '1728.46354.36.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '36.dy1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dy1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336363
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.a1', '18.bb1.a1'], 'contains': ['72.dv1.a1', '72.dy1.a1', '72.ed1.a1', '72.em1.a1', '72.ep1.a1', '72.eu1.b1', '72.ex1.b1', '108.bo1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5967, -1, 4045, -1, 3700, -1, 3899, -1], 'generators': [46999, 622537, 1634131, 817145, 887131], 'label': '1728.46354.36.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.dz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336364
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.dz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.b1', '18.bb1.a1'], 'contains': ['72.dv1.b1', '72.dy1.a1', '72.ed1.a1', '72.em1.b1', '72.ep1.b1', '72.eu1.a1', '72.ex1.a1', '108.bo1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5967, -1, 4182, -1, 3700, -1, 3869, -1], 'generators': [70957, 622537, 1634131, 817145, 887131], 'label': '1728.46354.36.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.dz1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dz1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336365
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.a1', '18.bc1.a1'], 'contains': ['72.dw1.a1', '72.dz1.a1', '72.ee1.a1', '72.en1.a1', '72.eq1.a1', '72.ev1.b1', '72.ey1.b1', '108.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': '36T2466', 'count': 18, 'diagramx': [6830, -1, 2906, -1, 3440, -1, 2935, -1], 'generators': [46999, 47089, 1634131, 817145, 887131], 'label': '1728.46354.36.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.ea1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336366
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.a1', '18.bc1.a1'], 'contains': ['72.dw1.a1', '72.dz1.a2', '72.ee1.a2', '72.en1.a2', '72.eq1.a2', '72.ev1.b2', '72.ey1.b2', '108.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': '36T2466', 'count': 18, 'diagramx': [6830, -1, 2927, -1, 3440, -1, 2965, -1], 'generators': [46999, 47089, 1656811, 817145, 887131], 'label': '1728.46354.36.ea1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.ea1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336367
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.b1', '18.bc1.a1'], 'contains': ['72.dw1.b1', '72.dz1.a1', '72.ee1.a2', '72.en1.b1', '72.eq1.b1', '72.ev1.a1', '72.ey1.a1', '108.bo1.b1'], 'core': '1728.a1.a1', 'coset_action_label': '36T2466', 'count': 18, 'diagramx': [6830, -1, 3148, -1, 3440, -1, 2874, -1], 'generators': [70957, 47089, 1634131, 817145, 887131], 'label': '1728.46354.36.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.ea1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336368
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.g1.a1', '12.s1.a1', '12.t1.a1', '12.bi1.a1', '12.bk1.a1', '12.bn1.a1', '12.cc1.a1', '18.bd1.a1', '18.be1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2959, -1, 6739, -1, 5665, -1, 6315, -1], 'generators': [46999, 887131, 793169, 835777, 622105, 70633, 622537], 'label': '1728.46354.6.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336369
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1.b1', '18.bc1.a1'], 'contains': ['72.dw1.b1', '72.dz1.a2', '72.ee1.a1', '72.en1.b2', '72.eq1.b2', '72.ev1.a2', '72.ey1.a2', '108.bo1.b1'], 'core': '1728.a1.a1', 'coset_action_label': '36T2466', 'count': 18, 'diagramx': [6830, -1, 3170, -1, 3440, -1, 2904, -1], 'generators': [70957, 47089, 1656811, 817145, 887131], 'label': '1728.46354.36.ea1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.ea1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.b2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336370
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.eb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.a1', '12.cq1.a1', '18.q1.a1'], 'contains': ['72.ef1.a1', '72.eg1.a1', '72.ej1.a1', '72.er1.a1', '72.ez1.a1', '72.fd1.a1', '72.fk1.a1', '108.bp1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8211, -1, 2709, -1, 3664, -1, 3124, -1], 'generators': [46999, 887131, 1674451, 70633, 622105], 'label': '1728.46354.36.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '36.eb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336371
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.eb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.b1', '12.cq1.b1', '18.q1.a1'], 'contains': ['72.ef1.b1', '72.eg1.b1', '72.ej1.b1', '72.er1.b1', '72.ez1.a1', '72.fd1.b1', '72.fk1.a1', '108.bp1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8211, -1, 2771, -1, 3664, -1, 3155, -1], 'generators': [793511, 887131, 1674451, 70633, 622105], 'label': '1728.46354.36.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '36.eb1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eb1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336372
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ec1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.a1', '12.cr1.a1', '18.r1.a1'], 'contains': ['72.d1.a1', '72.fa1.a1', '72.fm1.a1', '108.bp1.a1', '144.du1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9146, -1, 1334, -1, 1348, -1, 1386, -1], 'generators': [46999, 70633, 1674451, 1341703, 887131], 'label': '1728.46354.36.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.ec1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336373
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ec1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.b1', '12.cr1.b1', '18.r1.a1'], 'contains': ['72.d1.b1', '72.fa1.a1', '72.fm1.a1', '108.bp1.b1', '144.du1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9146, -1, 1547, -1, 1348, -1, 1502, -1], 'generators': [793511, 70633, 1674451, 1341703, 887131], 'label': '1728.46354.36.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.ec1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ec1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336374
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ed1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cq1.a1', '12.cr1.a1', '18.x1.a1'], 'contains': ['72.eh1.a1', '72.ei1.a1', '72.ek1.a1', '72.es1.a1', '72.fc1.a1', '72.fe1.a1', '72.fl1.a1', '108.bp1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8258, -1, 2737, -1, 3507, -1, 3186, -1], 'generators': [46999, 622537, 1674451, 70633, 887131], 'label': '1728.46354.36.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '36.ed1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336375
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '36.ed1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cq1.b1', '12.cr1.b1', '18.x1.a1'], 'contains': ['72.eh1.b1', '72.ei1.b1', '72.ek1.b1', '72.es1.b1', '72.fc1.a1', '72.fe1.b1', '72.fl1.a1', '108.bp1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8258, -1, 2793, -1, 3507, -1, 3253, -1], 'generators': [793511, 622537, 1674451, 70633, 887131], 'label': '1728.46354.36.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '36.ed1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ed1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336376
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ee1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.a1', '12.ct1.a1', '18.ba1.a1'], 'contains': ['72.el1.a1', '72.eo1.a1', '72.et1.a1', '72.ew1.a1', '72.fd1.a1', '72.fh1.a1', '72.fo1.a1', '108.bq1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7793, -1, 2217, -1, 3136, -1, 2651, -1], 'generators': [46999, 622105, 1634131, 70633, 887131], 'label': '1728.46354.36.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '36.ee1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336377
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ee1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.b1', '12.ct1.b1', '18.ba1.a1'], 'contains': ['72.el1.b1', '72.eo1.b1', '72.et1.b1', '72.ew1.b1', '72.fd1.b1', '72.fh1.a1', '72.fo1.a1', '108.bq1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7793, -1, 2050, -1, 3136, -1, 2681, -1], 'generators': [793511, 622105, 1634131, 70633, 887131], 'label': '1728.46354.36.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '36.ee1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ee1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336378
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.a1', '12.cu1.a1', '18.bb1.a1'], 'contains': ['72.em1.a1', '72.ep1.a1', '72.eu1.a1', '72.ex1.a1', '72.fe1.a1', '72.fi1.a1', '72.fp1.a1', '108.bq1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7862, -1, 2239, -1, 3050, -1, 2747, -1], 'generators': [46999, 622537, 1634131, 70633, 887131], 'label': '1728.46354.36.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.ef1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336379
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bp1.a1', '12.bw1.a1', '12.ct1.a1', '12.ct1.b1', '18.ba1.a1', '18.bf1.a1', '24.bn1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 2736, -1, 1816, -1, 1543, -1], 'generators': [46999, 887131, 622105, 1634131, 70633, 793169, 1341703], 'label': '1728.46354.6.v1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336380
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.b1', '12.cu1.b1', '18.bb1.a1'], 'contains': ['72.em1.b1', '72.ep1.b1', '72.eu1.b1', '72.ex1.b1', '72.fe1.b1', '72.fi1.a1', '72.fp1.a1', '108.bq1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7862, -1, 2072, -1, 3050, -1, 2812, -1], 'generators': [793511, 622537, 1634131, 70633, 887131], 'label': '1728.46354.36.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.ef1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ef1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336381
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.eg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.a1', '12.cv1.a1', '18.bc1.a1'], 'contains': ['72.en1.a1', '72.eq1.a2', '72.ev1.a1', '72.ey1.a2', '72.ff1.a1', '72.fj1.a1', '72.fq1.a1', '108.bq1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7896, -1, 2029, -1, 3013, -1, 2315, -1], 'generators': [46999, 47089, 1634131, 70633, 887131], 'label': '1728.46354.36.eg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.eg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336382
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.eg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.a1', '12.cv1.a2', '18.bc1.a1'], 'contains': ['72.en1.a2', '72.eq1.a1', '72.ev1.a2', '72.ey1.a1', '72.ff1.a1', '72.fj1.a2', '72.fq1.a2', '108.bq1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7896, -1, 2006, -1, 3013, -1, 2346, -1], 'generators': [46999, 1197949, 1634131, 70633, 887131], 'label': '1728.46354.36.eg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.eg1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eg1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336383
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.eg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.b1', '12.cv1.b1', '18.bc1.a1'], 'contains': ['72.en1.b1', '72.eq1.b2', '72.ev1.b1', '72.ey1.b2', '72.ff1.b1', '72.fj1.a1', '72.fq1.a2', '108.bq1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7896, -1, 1888, -1, 3013, -1, 2376, -1], 'generators': [793511, 47089, 1634131, 70633, 887131], 'label': '1728.46354.36.eg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.eg1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eg1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336384
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '36.eg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1.b1', '12.cv1.b2', '18.bc1.a1'], 'contains': ['72.en1.b2', '72.eq1.b1', '72.ev1.b2', '72.ey1.b1', '72.ff1.b1', '72.fj1.a2', '72.fq1.a1', '108.bq1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7896, -1, 1942, -1, 3013, -1, 2406, -1], 'generators': [793511, 1197949, 1634131, 70633, 887131], 'label': '1728.46354.36.eg1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '36.eg1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eg1.b2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336385
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.eh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1.a1', '12.cu1.a1', '12.cv1.a1', '12.cv1.a2', '18.bf1.a1'], 'contains': ['72.d1.a1', '72.fg1.a1', '72.fr1.a1', '108.bq1.a1', '144.ee1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8845, -1, 503, -1, 581, -1, 424, -1], 'generators': [46999, 70633, 1634131, 1341703, 887131], 'label': '1728.46354.36.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '36.eh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336386
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '36.eh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1.b1', '12.cu1.b1', '12.cv1.b1', '12.cv1.b2', '18.bf1.a1'], 'contains': ['72.d1.b1', '72.fg1.a1', '72.fr1.a1', '108.bq1.b1', '144.ee1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8845, -1, 117, -1, 581, -1, 454, -1], 'generators': [793511, 70633, 1634131, 1341703, 887131], 'label': '1728.46354.36.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '36.eh1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eh1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336387
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '12.c1.a1', 'complements': ['36.eh1.a1', '36.eh1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.d1.a1', '24.g1.a1', '24.bb1.a1', '24.be1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '96.k1.a1', '144.a1.a1', '144.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3838, 9272, 8137, 811, 8334, 8801, 8899, 2800], 'generators': [1674451, 793169, 622105, 622537], 'label': '1728.46354.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.d1.a1'], 'normal_contains': ['96.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336388
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '36.b1.a1', 'complements': ['36.ec1.a1', '36.ec1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.j1.a1', '24.bj1.a1', '24.bs1.a1', '24.by1.a1'], 'contains': ['96.a1.a1', '96.v1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3632, 8455, 9043, 2351, 8006, 8072, 8336, 2121], 'generators': [1634131, 793169, 622537, 622105], 'label': '1728.46354.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.e1.a1', '24.d1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336389
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '12.d1.a1', 'complements': ['36.ec1.a1', '36.ec1.b1', '36.eh1.a1', '36.eh1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.d1.a1', '24.n1.a1', '24.bl1.a1', '24.bt1.a1', '24.ca1.a1'], 'contains': ['96.a1.a1', '144.b1.a1', '144.bl1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [761, 7353, 7301, 1543, 8162, 7088, 8701, 1369], 'generators': [835777, 622537, 793169, 622105], 'label': '1728.46354.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.g1.a1', '24.d1.a1'], 'normal_contains': ['96.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336390
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.c1.a1'], 'contains': ['12.d1.a1', '12.bq1.a1', '12.by1.a1', '12.cu1.a1', '12.cu1.b1', '18.bb1.a1', '18.bf1.a1', '24.bo1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7249, -1, 2353, -1, 1425, -1, 1890, -1], 'generators': [46999, 887131, 622537, 1634131, 70633, 793169, 1341703], 'label': '1728.46354.6.w1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336391
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': ['36.dp1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.cx1.a1', '24.da1.a1', '24.da1.b1', '24.df1.a1', '24.dg1.a1', '24.dk1.a1'], 'contains': ['96.i1.a1', '144.c1.a1', '144.d1.a1', '144.dp1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8150, 5535, 2317, 4903, 2868, 5361, 2363, 5381], 'generators': [887131, 70633, 622537, 622105], 'label': '1728.46354.48.d1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['144.c1.a1', '144.d1.a1', '192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '24.14', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336392
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.a1.a1', 'complements': ['36.dq1.a1', '36.dv1.a1', '36.dr1.a1', '36.du1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.e1.b1', '24.cw1.a1', '24.dc1.a1', '24.dh1.a1', '24.dl1.a1'], 'contains': ['144.c1.a1', '144.e1.a1', '144.dq1.a1', '192.b1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9526, 1933, 1031, 8594, 831, 2774, 406, 6573], 'generators': [1341703, 622105, 887131, 70633], 'label': '1728.46354.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.e1.b1'], 'normal_contains': ['144.c1.a1', '144.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336393
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '48.c1.a1', 'complements': ['36.dn1.a1', '36.dt1.a1', '36.do1.a1', '36.ds1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1', '24.cy1.a1', '24.dd1.a1', '24.dj1.a1', '24.dn1.a1'], 'contains': ['144.d1.a1', '144.e1.a1', '144.dr1.a1', '192.d1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8945, 3080, 803, 5974, 795, 4077, 926, 7180], 'generators': [1341703, 622537, 887131, 70633], 'label': '1728.46354.48.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': ['16.a1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1'], 'normal_contains': ['144.d1.a1', '144.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336394
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1'], 'contains': ['96.a1.a1', '96.h1.a1', '96.i1.a1', '144.f1.a1', '144.g1.a1', '144.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2628, -1, 7340, -1, 7671, -1, 7977, -1], 'generators': [793169, 887131, 622537, 622105], 'label': '1728.46354.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336395
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '16.b1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1'], 'contains': ['96.b1.a1', '96.j1.a1', '144.i1.a1', '144.j1.a1', '144.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7719, -1, 3340, -1, 1925, -1, 1882, -1], 'generators': [1674451, 793169, 1341703, 622105], 'label': '1728.46354.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '48.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336396
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.b1.a1', '24.bc1.a1', '24.bd1.a1', '24.bg1.a1'], 'contains': ['96.d1.a1', '96.l1.a1', '144.a1.a1', '144.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7042, -1, 3298, -1, 1896, -1, 1942, -1], 'generators': [1674451, 793169, 1341703, 622537], 'label': '1728.46354.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336397
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '16.b1.a1', '24.bh1.a1'], 'contains': ['96.e1.a1', '96.m1.a1', '144.a1.a1', '144.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7849, -1, 2462, -1, 594, -1, 1092, -1], 'generators': [1674451, 793169, 766291, 622537], 'label': '1728.46354.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '48.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336398
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.h1.a1', '24.bb1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bl1.a1', '24.bm1.a1'], 'contains': ['96.a1.a1', '96.n1.a1', '96.n1.b1', '144.l1.a1', '144.m1.a1', '144.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [941, -1, 9787, -1, 9129, -1, 9255, -1], 'generators': [46999, 793169, 622537, 622105], 'label': '1728.46354.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336399
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.c1.a1', '24.y1.a1', '24.bn1.a1', '24.bq1.a1'], 'contains': ['96.b1.a1', '96.o1.a1', '96.o1.b1', '144.l1.a1', '144.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8460, -1, 2533, -1, 1964, -1, 1528, -1], 'generators': [46999, 793169, 622105, 1341703], 'label': '1728.46354.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336400
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '16.c1.a1', '24.bc1.a1', '24.bo1.a1', '24.br1.a1'], 'contains': ['96.d1.a1', '96.p1.a1', '96.p1.b1', '144.m1.a1', '144.o1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7506, -1, 2378, -1, 1783, -1, 1765, -1], 'generators': [46999, 793169, 622537, 1341703], 'label': '1728.46354.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336401
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['12.bo1.a1', '12.br1.a1', '12.ca1.a1', '12.cv1.a1', '12.cv1.a2', '12.cv1.b1', '12.cv1.b2', '18.bc1.a1', '18.bf1.a1', '24.bp1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8344, -1, 912, -1, 1147, -1, 588, -1], 'generators': [46999, 887131, 47089, 1634131, 70633, 793169, 1341703], 'label': '1728.46354.6.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '6.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.x1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336402
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '16.c1.a1', '24.bp1.a1'], 'contains': ['96.f1.a1', '96.q1.a1', '96.q1.b1', '144.n1.a1', '144.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8674, -1, 870, -1, 1118, -1, 712, -1], 'generators': [46999, 793169, 47089, 1341703], 'label': '1728.46354.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '48.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336403
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.i1.a1', '24.bi1.a1', '24.bs1.a1', '24.bt1.a1', '24.bu1.a1', '24.bv1.a1'], 'contains': ['96.a1.a1', '96.r1.a1', '144.p1.a1', '144.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [912, -1, 8943, -1, 9514, -1, 9471, -1], 'generators': [835273, 793169, 622105, 622537], 'label': '1728.46354.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336404
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '16.d1.a1', '24.z1.a1', '24.bn1.a1', '24.bw1.a1'], 'contains': ['96.b1.a1', '96.s1.a1', '144.r1.a1', '144.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7267, -1, 3452, -1, 1819, -1, 1625, -1], 'generators': [1634131, 793169, 1341703, 622105], 'label': '1728.46354.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '48.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336405
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '16.d1.a1', '24.bd1.a1', '24.bo1.a1', '24.bx1.a1'], 'contains': ['96.d1.a1', '96.t1.a1', '144.r1.a1', '144.t1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7077, -1, 3400, -1, 1747, -1, 1841, -1], 'generators': [1634131, 793169, 1341703, 622537], 'label': '1728.46354.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '48.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336406
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '16.d1.a1', '24.bp1.a1'], 'contains': ['96.f1.a1', '96.u1.a1', '96.u1.a2', '144.r1.a1', '144.u1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8425, -1, 1094, -1, 1082, -1, 682, -1], 'generators': [1634131, 793169, 1341703, 47089], 'label': '1728.46354.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336407
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.k1.a1', '24.bb1.a1', '24.bi1.a1', '24.by1.a1', '24.bz1.a1', '24.ca1.a1', '24.cb1.a1'], 'contains': ['96.a1.a1', '96.w1.a1', '144.v1.a1', '144.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [970, -1, 9757, -1, 9551, -1, 9619, -1], 'generators': [1675405, 793169, 622105, 622537], 'label': '1728.46354.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336408
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '16.e1.a1', '24.y1.a1', '24.bw1.a1', '24.cc1.a1'], 'contains': ['96.b1.a1', '96.x1.a1', '144.v1.a1', '144.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8368, -1, 3541, -1, 2328, -1, 3767, -1], 'generators': [1675405, 793169, 622105, 1341703], 'label': '1728.46354.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '48.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336409
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '16.e1.a1', '24.cd1.a1'], 'contains': ['96.c1.a1', '96.y1.a1', '144.v1.a1', '144.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8748, -1, 2688, -1, 2132, -1, 5790, -1], 'generators': [1675405, 793169, 622105, 767155], 'label': '1728.46354.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '48.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336410
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '16.e1.a1', '24.bc1.a1', '24.bx1.a1', '24.ce1.a1'], 'contains': ['96.d1.a1', '96.z1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7215, -1, 2813, -1, 2172, -1, 4735, -1], 'generators': [1675405, 793169, 1341703, 622537], 'label': '1728.46354.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336411
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.l1.a1', '24.be1.a1', '24.bk1.a1', '24.bt1.a1', '24.bu1.a1', '24.bz1.a1'], 'contains': ['96.a1.a1', '96.ba1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1554, -1, 8968, -1, 9096, -1, 9119, -1], 'generators': [793657, 793169, 622537, 622105], 'label': '1728.46354.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336412
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '6.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 36, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.c1.a1'], 'contains': ['12.d1.a1', '12.ce1.a1', '12.cf1.a1', '18.be1.a1', '18.bg1.a1', '24.br1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4590, -1, 5535, -1, 2678, -1, 3472, -1], 'generators': [46999, 887131, 1341703, 835777, 70633, 622537, 793169], 'label': '1728.46354.6.y1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.y1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336413
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.m1.a1', '24.bf1.a1', '24.bj1.a1', '24.bk1.a1', '24.bv1.a1', '24.ca1.a1', '24.cb1.a1'], 'contains': ['96.a1.a1', '96.bb1.a1', '144.bc1.a1', '144.bd1.a1', '144.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [378, -1, 9488, -1, 8399, -1, 8835, -1], 'generators': [1633789, 793169, 622537, 622105], 'label': '1728.46354.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336414
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '16.f1.a1', '24.ba1.a1', '24.bn1.a1', '24.cc1.a1'], 'contains': ['96.b1.a1', '96.bc1.a1', '144.bc1.a1', '144.bf1.a1', '144.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7626, -1, 2999, -1, 1423, -1, 1430, -1], 'generators': [1633789, 793169, 1341703, 622105], 'label': '1728.46354.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '48.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336415
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '16.f1.a1', '24.cd1.a1'], 'contains': ['96.c1.a1', '96.bd1.a1', '144.bc1.a1', '144.bh1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8588, -1, 2712, -1, 1216, -1, 1694, -1], 'generators': [1633789, 793169, 767155, 622105], 'label': '1728.46354.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '48.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336416
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '16.f1.a1', '24.bg1.a1', '24.bo1.a1', '24.ce1.a1'], 'contains': ['96.d1.a1', '96.be1.a1', '144.bd1.a1', '144.bf1.a1', '144.bh1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7011, -1, 2769, -1, 1359, -1, 1799, -1], 'generators': [1633789, 793169, 1341703, 622537], 'label': '1728.46354.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '48.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336417
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '16.f1.a1', '24.bh1.a1'], 'contains': ['96.e1.a1', '96.bf1.a1', '144.bd1.a1', '144.bg1.a1', '144.bi1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7811, -1, 2432, -1, 422, -1, 857, -1], 'generators': [1633789, 793169, 766291, 622537], 'label': '1728.46354.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1.a1', 'old_label': '48.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336418
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '16.f1.a1', '24.bp1.a1'], 'contains': ['96.f1.a1', '96.bg1.a1', '96.bg1.a2', '144.be1.a1', '144.bf1.a1', '144.bi1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8719, -1, 846, -1, 744, -1, 615, -1], 'generators': [1633789, 793169, 1341703, 47089], 'label': '1728.46354.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336419
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.13', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '16.f1.a1'], 'contains': ['96.g1.a1', '96.bh1.a1', '96.bh1.a2', '144.be1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8622, -1, 1614, -1, 467, -1, 783, -1], 'generators': [1633789, 793169, 766291, 47089], 'label': '1728.46354.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1.a1', 'old_label': '48.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336420
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.p1.a1', '24.be1.a1', '24.bm1.a1', '24.bs1.a1', '24.bu1.a1', '24.cb1.a1'], 'contains': ['96.a1.a1', '144.bj1.a1', '144.bm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1415, -1, 8919, -1, 9362, -1, 9505, -1], 'generators': [1674955, 622537, 793169, 622105], 'label': '1728.46354.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336421
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.q1.a1', '24.bf1.a1', '24.bl1.a1', '24.bm1.a1', '24.bv1.a1', '24.by1.a1', '24.bz1.a1'], 'contains': ['96.a1.a1', '144.bk1.a1', '144.bn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [103, -1, 8095, -1, 8867, -1, 9156, -1], 'generators': [834823, 622537, 793169, 622105], 'label': '1728.46354.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336422
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '16.g1.a1', '24.z1.a1', '24.bq1.a1', '24.cc1.a1'], 'contains': ['96.b1.a1', '144.b1.a1', '144.bo1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4909, -1, 4326, -1, 2457, -1, 3713, -1], 'generators': [835777, 1341703, 793169, 622105], 'label': '1728.46354.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336423
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.i1.a1', '12.bp1.a1', '12.bt1.a1', '18.bh1.a1', '18.bi1.a1', '24.bw1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6667, -1, 5574, -1, 2815, -1, 3418, -1], 'generators': [834823, 887131, 622105, 1634131, 70633, 793169, 1341703], 'label': '1728.46354.6.z1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.z1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336424
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '16.h1.a1', '24.ba1.a1', '24.bq1.a1', '24.bw1.a1'], 'contains': ['96.b1.a1', '144.bk1.a1', '144.bp1.a1', '144.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6744, -1, 5716, -1, 2611, -1, 2385, -1], 'generators': [834823, 793169, 1341703, 622105], 'label': '1728.46354.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336425
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '16.g1.a1', '24.cd1.a1'], 'contains': ['96.c1.a1', '144.b1.a1', '144.br1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6964, -1, 3031, -1, 2288, -1, 5896, -1], 'generators': [835777, 767155, 793169, 622105], 'label': '1728.46354.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '48.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336426
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '16.g1.a1', '24.bd1.a1', '24.br1.a1', '24.ce1.a1'], 'contains': ['96.d1.a1', '144.bl1.a1', '144.bo1.a1', '144.br1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4942, -1, 3601, -1, 2379, -1, 4071, -1], 'generators': [835777, 1341703, 622537, 793169], 'label': '1728.46354.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '48.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336427
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '16.h1.a1', '24.bg1.a1', '24.br1.a1', '24.bx1.a1'], 'contains': ['96.d1.a1', '144.bn1.a1', '144.bp1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5528, -1, 5658, -1, 2548, -1, 3192, -1], 'generators': [834823, 622537, 793169, 1341703], 'label': '1728.46354.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '48.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336428
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.a1', '16.h1.a1', '24.bh1.a1'], 'contains': ['96.e1.a1', '144.bn1.a1', '144.bq1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7430, -1, 3695, -1, 2040, -1, 1180, -1], 'generators': [834823, 622537, 793169, 766291], 'label': '1728.46354.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1.a1', 'old_label': '48.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336429
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.cf1.a1', '24.cj1.a1'], 'contains': ['96.h1.a1', '96.k1.a1', '96.r1.a1', '144.bs1.a1', '144.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3756, -1, 8348, -1, 9230, -1, 9441, -1], 'generators': [1674451, 1633643, 622105, 622537], 'label': '1728.46354.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.bm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336430
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.cf1.a1', '24.cg1.a1'], 'contains': ['96.h1.a1', '96.n1.a1', '96.n1.b1', '144.bu1.a1', '144.bv1.a1', '144.bw1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2221, -1, 9740, -1, 9741, -1, 9755, -1], 'generators': [46999, 1633643, 622537, 622105], 'label': '1728.46354.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336431
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.ch1.a1', '24.cj1.a1'], 'contains': ['96.h1.a1', '96.r1.a1', '144.bx1.a1', '144.by1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1149, -1, 6639, -1, 9194, -1, 9411, -1], 'generators': [1651771, 1633643, 622105, 622537], 'label': '1728.46354.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '48.bo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336432
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.cg1.a1', '24.cl1.a1'], 'contains': ['96.h1.a1', '96.v1.a1', '96.ba1.a1', '144.bz1.a1', '144.ca1.a1', '144.cb1.a1', '144.cb1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3793, -1, 9273, -1, 8051, -1, 8114, -1], 'generators': [1634131, 1633643, 622537, 622105], 'label': '1728.46354.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.bp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336433
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.cf1.a1', '24.ci1.a1'], 'contains': ['96.h1.a1', '96.w1.a1', '144.cc1.a1', '144.cd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3111, -1, 9620, -1, 9984, -1, 9987, -1], 'generators': [1675405, 1633643, 622105, 622537], 'label': '1728.46354.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.bq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336434
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3456.ma', 'aut_weyl_index': 2, 'centralizer': '864.a1.a1', 'complements': ['864.d1.a1', '864.f1.a1', '864.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.j1.a1', '4.j1.b1', '6.t1.a1', '6.v1.a1', '6.w1.a1', '6.x1.a1', '8.f1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7542, 2490, 2445, 6851, 1532, 2852, 1615, 3708], 'generators': [46999, 622537, 622105, 1634131, 1341703, 70633, 887131, 793169], 'label': '1728.46354.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '864.4673', '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': '864.4673'}
  • id: 264336435
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.c1.a1'], 'contains': ['12.f1.a1', '12.bq1.a1', '12.cf1.a1', '18.bh1.a1', '18.bj1.a1', '24.bx1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5761, -1, 5503, -1, 2712, -1, 3581, -1], 'generators': [834823, 887131, 622537, 1634131, 70633, 793169, 1341703], 'label': '1728.46354.6.ba1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336436
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.ci1.a1', '24.cl1.a1'], 'contains': ['96.h1.a1', '96.ba1.a1', '144.ce1.a1', '144.cf1.a1', '144.cg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3246, -1, 6777, -1, 8443, -1, 8603, -1], 'generators': [1656811, 1633643, 622537, 622105], 'label': '1728.46354.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.br1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336437
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.cg1.a1', '24.ch1.a1'], 'contains': ['96.h1.a1', '96.bb1.a1', '144.ch1.a1', '144.ci1.a1', '144.cj1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1329, -1, 9589, -1, 9474, -1, 9342, -1], 'generators': [1633789, 1633643, 622537, 622105], 'label': '1728.46354.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.bs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336438
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.ch1.a1', '24.ci1.a1'], 'contains': ['96.h1.a1', '144.ck1.a1', '144.cl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2347, -1, 9551, -1, 9799, -1, 9803, -1], 'generators': [812125, 622537, 1633643, 622105], 'label': '1728.46354.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.bt1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336439
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.cj1.a1', '24.ck1.a1', '24.ck1.b1', '24.cl1.a1', '24.cm1.a1', '24.cn1.a1'], 'contains': ['96.h1.a1', '96.i1.a1', '144.cm1.a1', '144.cn1.a1', '144.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5553, -1, 4555, -1, 4266, -1, 4578, -1], 'generators': [817145, 887131, 622537, 622105], 'label': '1728.46354.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336440
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.cj1.a1', '24.co1.a1', '24.co1.b1', '24.cp1.a1', '24.cp1.b1', '24.cx1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.r1.a1', '144.cp1.a1', '144.cq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6320, -1, 4892, -1, 5327, -1, 5694, -1], 'generators': [1674451, 887131, 622105, 622537], 'label': '1728.46354.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.bv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336441
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.ck1.a1', '24.co1.a1', '24.cq1.a1', '24.cr1.a1', '24.cs1.a1', '24.da1.a1'], 'contains': ['96.i1.a1', '96.n1.a1', '144.cr1.a1', '144.cs1.a1', '144.ct1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6299, -1, 4424, -1, 4389, -1, 4559, -1], 'generators': [46999, 887131, 622537, 622105], 'label': '1728.46354.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336442
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.ck1.b1', '24.co1.b1', '24.cq1.b1', '24.cr1.b1', '24.cs1.b1', '24.da1.b1'], 'contains': ['96.i1.a1', '96.n1.b1', '144.cr1.b1', '144.cs1.b1', '144.ct1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6299, -1, 4574, -1, 4389, -1, 4828, -1], 'generators': [793511, 887131, 622537, 622105], 'label': '1728.46354.48.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bw1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336443
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.cj1.a1', '24.cq1.a1', '24.cq1.b1', '24.ct1.a1', '24.ct1.b1', '24.cx1.a1'], 'contains': ['96.i1.a1', '96.r1.a1', '144.cu1.a1', '144.cv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6618, -1, 5002, -1, 4701, -1, 5463, -1], 'generators': [1651771, 887131, 622105, 622537], 'label': '1728.46354.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.bx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336444
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.cl1.a1', '24.cr1.a1', '24.cr1.b1', '24.cu1.a1', '24.cu1.b1', '24.df1.a1'], 'contains': ['96.i1.a1', '96.v1.a1', '96.ba1.a1', '144.cw1.a1', '144.cx1.a1', '144.cy1.a1', '144.cy1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5829, -1, 3997, -1, 4191, -1, 4139, -1], 'generators': [1634131, 887131, 622537, 622105], 'label': '1728.46354.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.by1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336445
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.cm1.a1', '24.co1.a1', '24.co1.b1', '24.ct1.a1', '24.ct1.b1', '24.dg1.a1'], 'contains': ['96.i1.a1', '96.w1.a1', '144.cz1.a1', '144.da1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6485, -1, 4920, -1, 5123, -1, 5760, -1], 'generators': [1675405, 887131, 622105, 622537], 'label': '1728.46354.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.bz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336446
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.z1.a1', '12.bb1.a1', '12.bc1.a1', '12.bg1.a1', '12.bs1.a1', '12.cc1.a1', '18.bi1.a1', '18.bj1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4832, -1, 6703, -1, 5561, -1, 6158, -1], 'generators': [834823, 622537, 887131, 1634131, 622105, 70633, 793169], 'label': '1728.46354.6.bb1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336447
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.cl1.a1', '24.cs1.a1', '24.cs1.b1', '24.cv1.a1', '24.cv1.b1', '24.df1.a1'], 'contains': ['96.i1.a1', '96.ba1.a1', '144.db1.a1', '144.dc1.a1', '144.dd1.a1', '144.dd1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5789, -1, 4084, -1, 3903, -1, 3626, -1], 'generators': [1656811, 887131, 622537, 622105], 'label': '1728.46354.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.ca1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336448
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.cn1.a1', '24.cr1.a1', '24.cr1.b1', '24.cv1.a1', '24.cv1.b1', '24.dk1.a1'], 'contains': ['96.i1.a1', '96.bb1.a1', '144.de1.a1', '144.df1.a1', '144.dg1.a1', '144.dg1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6081, -1, 3939, -1, 3859, -1, 3994, -1], 'generators': [1633789, 887131, 622537, 622105], 'label': '1728.46354.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.cb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336449
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.ck1.b1', '24.cp1.a1', '24.ct1.a1', '24.cu1.a1', '24.cv1.a1', '24.da1.a1'], 'contains': ['96.i1.a1', '144.dh1.a1', '144.dk1.a1', '144.dn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6426, -1, 4475, -1, 3984, -1, 4231, -1], 'generators': [70957, 622537, 622105, 887131], 'label': '1728.46354.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.cc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336450
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.ck1.a1', '24.cp1.b1', '24.ct1.b1', '24.cu1.b1', '24.cv1.b1', '24.da1.b1'], 'contains': ['96.i1.a1', '144.dh1.b1', '144.dk1.b1', '144.dn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6426, -1, 4405, -1, 3984, -1, 4194, -1], 'generators': [817469, 622537, 622105, 887131], 'label': '1728.46354.48.cc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.cc1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336451
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '24.cm1.a1', '24.cp1.a1', '24.cp1.b1', '24.cq1.a1', '24.cq1.b1', '24.dg1.a1'], 'contains': ['96.i1.a1', '144.di1.a1', '144.dl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6694, -1, 4850, -1, 4422, -1, 5074, -1], 'generators': [1651447, 622105, 887131, 622537], 'label': '1728.46354.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.cd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336452
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.cn1.a1', '24.cs1.a1', '24.cs1.b1', '24.cu1.a1', '24.cu1.b1', '24.dk1.a1'], 'contains': ['96.i1.a1', '144.dj1.a1', '144.dm1.a1', '144.do1.a1', '144.do1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6009, -1, 3893, -1, 3380, -1, 3413, -1], 'generators': [1656487, 887131, 622537, 622105], 'label': '1728.46354.48.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.ce1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 264336453
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.u1.a1', '24.di1.a1', '24.dm1.a1'], 'contains': ['144.c1.a1', '144.dr1.a1', '144.ds1.a1', '192.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9929, -1, 1072, -1, 518, -1, 1009, -1], 'generators': [767155, 622105, 887131, 70633], 'label': '1728.46354.48.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '48.cf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336454
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.v1.a1', '24.cz1.a1', '24.do1.a1'], 'contains': ['144.d1.a1', '144.dq1.a1', '144.ds1.a1', '192.e1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9491, -1, 307, -1, 90, -1, 287, -1], 'generators': [766291, 622537, 887131, 70633], 'label': '1728.46354.48.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.cg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336455
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 144, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.w1.a1', '24.db1.a1', '24.db1.b1', '24.de1.a1', '24.de1.a2', '24.dp1.a1', '24.dp1.a2'], 'contains': ['144.e1.a1', '144.dp1.a1', '144.ds1.a1', '192.f1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9972, -1, 33, -1, 290, -1, 13, -1], 'generators': [1341703, 47089, 887131, 70633], 'label': '1728.46354.48.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '48.ch1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 264336456
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.x1.a1', '24.dq1.a1', '24.dq1.a2'], 'contains': ['144.dp1.a1', '144.dq1.a1', '144.dr1.a1', '144.ds1.a1', '192.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9872, -1, 134, -1, 197, -1, 167, -1], 'generators': [766291, 47089, 887131, 70633], 'label': '1728.46354.48.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '48.ci1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336457
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.g1.a1', '12.bd1.a1', '12.be1.a1', '12.bh1.a1', '12.bj1.a1', '12.bs1.a1', '12.bv1.a1', '18.bk1.a1', '18.bl1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4870, -1, 5809, -1, 5510, -1, 6268, -1], 'generators': [1675405, 622537, 887131, 835777, 622105, 70633, 793169], 'label': '1728.46354.6.bc1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336458
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.a1', '16.i1.a1', '24.y1.a1'], 'contains': ['96.j1.a1', '96.o1.a1', '96.x1.a1', '144.dt1.a1', '144.du1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9730, -1, 1385, -1, 1542, -1, 1498, -1], 'generators': [46999, 1674451, 622105, 1341703], 'label': '1728.46354.48.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '48.cj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336459
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1.b1', '16.i1.b1', '24.y1.a1'], 'contains': ['96.j1.a1', '96.o1.b1', '96.x1.a1', '144.dt1.b1', '144.du1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9730, -1, 1723, -1, 1542, -1, 1559, -1], 'generators': [793511, 1674451, 622105, 1341703], 'label': '1728.46354.48.cj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '48.cj1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336460
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.bb1.a1', '24.cf1.a1', '24.co1.a1'], 'contains': ['96.k1.a1', '96.n1.a1', '96.w1.a1', '144.dt1.a1', '144.dv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4652, -1, 9722, -1, 9158, -1, 9559, -1], 'generators': [46999, 1674451, 622105, 622537], 'label': '1728.46354.48.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.ck1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336461
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.bb1.a1', '24.cf1.a1', '24.co1.b1'], 'contains': ['96.k1.a1', '96.n1.b1', '96.w1.a1', '144.dt1.b1', '144.dv1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4652, -1, 9668, -1, 9158, -1, 9589, -1], 'generators': [793511, 1674451, 622105, 622537], 'label': '1728.46354.48.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.ck1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336462
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1.a1', '16.i1.a1', '24.bc1.a1'], 'contains': ['96.l1.a1', '96.p1.a1', '96.z1.a1', '144.du1.a1', '144.dv1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9249, -1, 1245, -1, 1503, -1, 1583, -1], 'generators': [46999, 1674451, 1341703, 622537], 'label': '1728.46354.48.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '48.cl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336463
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1.b1', '16.i1.b1', '24.bc1.a1'], 'contains': ['96.l1.a1', '96.p1.b1', '96.z1.a1', '144.du1.b1', '144.dv1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9249, -1, 1412, -1, 1503, -1, 1601, -1], 'generators': [793511, 1674451, 1341703, 622537], 'label': '1728.46354.48.cl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '48.cl1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336464
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '24.cf1.a1', '24.co1.a1'], 'contains': ['96.n1.a1', '96.r1.a1', '96.w1.a1', '144.dw1.a1', '144.dx1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3412, -1, 9994, -1, 9864, -1, 9891, -1], 'generators': [46999, 835273, 622105, 622537], 'label': '1728.46354.48.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.cm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336465
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '24.cf1.a1', '24.co1.b1'], 'contains': ['96.n1.b1', '96.r1.a1', '96.w1.a1', '144.dw1.b1', '144.dx1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3412, -1, 9961, -1, 9864, -1, 9922, -1], 'generators': [793511, 835273, 622105, 622537], 'label': '1728.46354.48.cm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.cm1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336466
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.bj1.a1', '24.cg1.a1', '24.cr1.a1'], 'contains': ['96.n1.a1', '96.v1.a1', '96.bb1.a1', '144.dy1.a1', '144.dz1.a1', '144.ea1.a1', '144.ea1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4095, -1, 9326, -1, 7746, -1, 8005, -1], 'generators': [46999, 1634131, 622537, 622105], 'label': '1728.46354.48.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.cn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336467
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.bj1.a1', '24.cg1.a1', '24.cr1.b1'], 'contains': ['96.n1.b1', '96.v1.a1', '96.bb1.a1', '144.dy1.b1', '144.dz1.b1', '144.ea1.b1', '144.ea1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4095, -1, 9358, -1, 7746, -1, 8042, -1], 'generators': [793511, 1634131, 622537, 622105], 'label': '1728.46354.48.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.cn1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336468
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.h1.a1', '12.bt1.a1', '12.bw1.a1', '18.bk1.a1', '18.bm1.a1', '24.cc1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6896, -1, 4165, -1, 2596, -1, 3556, -1], 'generators': [1675405, 887131, 622105, 835777, 70633, 793169, 1341703], 'label': '1728.46354.6.bd1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336469
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '24.cg1.a1', '24.cr1.a1'], 'contains': ['96.n1.a1', '96.ba1.a1', '96.bb1.a1', '144.eb1.a1', '144.ec1.a1', '144.ed1.a1', '144.ed1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2275, -1, 9644, -1, 8936, -1, 8933, -1], 'generators': [46999, 793657, 622537, 622105], 'label': '1728.46354.48.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.co1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336470
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '24.cg1.a1', '24.cr1.b1'], 'contains': ['96.n1.b1', '96.ba1.a1', '96.bb1.a1', '144.eb1.b1', '144.ec1.b1', '144.ed1.b1', '144.ed1.b2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2275, -1, 9698, -1, 8936, -1, 9006, -1], 'generators': [793511, 793657, 622537, 622105], 'label': '1728.46354.48.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.co1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336471
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1.a1', '16.j1.a1', '24.bn1.a1'], 'contains': ['96.o1.a1', '96.s1.a1', '96.bc1.a1', '144.dy1.a1', '144.ee1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8847, -1, 820, -1, 961, -1, 811, -1], 'generators': [46999, 1634131, 1341703, 622105], 'label': '1728.46354.48.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1.a1', 'old_label': '48.cp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336472
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1.b1', '16.j1.b1', '24.bn1.a1'], 'contains': ['96.o1.b1', '96.s1.a1', '96.bc1.a1', '144.dy1.b1', '144.ee1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8847, -1, 694, -1, 961, -1, 829, -1], 'generators': [793511, 1634131, 1341703, 622105], 'label': '1728.46354.48.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1.a1', 'old_label': '48.cp1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336473
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cu1.a1', '16.j1.a1', '24.bo1.a1'], 'contains': ['96.p1.a1', '96.t1.a1', '96.be1.a1', '144.dz1.a1', '144.ee1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8786, -1, 663, -1, 860, -1, 893, -1], 'generators': [46999, 1634131, 1341703, 622537], 'label': '1728.46354.48.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1.a1', 'old_label': '48.cq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336474
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cu1.b1', '16.j1.b1', '24.bo1.a1'], 'contains': ['96.p1.b1', '96.t1.a1', '96.be1.a1', '144.dz1.b1', '144.ee1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8786, -1, 542, -1, 860, -1, 950, -1], 'generators': [793511, 1634131, 1341703, 622537], 'label': '1728.46354.48.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1.a1', 'old_label': '48.cq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336475
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1.a1', '16.j1.a1', '24.bp1.a1'], 'contains': ['96.q1.a1', '96.u1.a1', '96.bg1.a1', '144.ea1.a1', '144.ee1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9394, -1, 427, -1, 644, -1, 533, -1], 'generators': [46999, 1634131, 1341703, 47089], 'label': '1728.46354.48.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.cr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336476
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1.a2', '16.j1.a1', '24.bp1.a1'], 'contains': ['96.q1.a1', '96.u1.a2', '96.bg1.a2', '144.ea1.a2', '144.ee1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9394, -1, 460, -1, 644, -1, 551, -1], 'generators': [46999, 1634131, 1341703, 1197949], 'label': '1728.46354.48.cr1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.cr1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336477
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1.b1', '16.j1.b1', '24.bp1.a1'], 'contains': ['96.q1.b1', '96.u1.a1', '96.bg1.a2', '144.ea1.b1', '144.ee1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9394, -1, 375, -1, 644, -1, 569, -1], 'generators': [793511, 1634131, 1341703, 47089], 'label': '1728.46354.48.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.cr1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336478
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1.b2', '16.j1.b1', '24.bp1.a1'], 'contains': ['96.q1.b1', '96.u1.a2', '96.bg1.a1', '144.ea1.b2', '144.ee1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9394, -1, 354, -1, 644, -1, 587, -1], 'generators': [793511, 1634131, 1341703, 1197949], 'label': '1728.46354.48.cr1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '48.cr1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.b2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336479
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '6.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['12.bu1.a1', '12.bx1.a1', '12.cd1.a1', '18.bk1.a1', '18.bn1.a1', '24.cd1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8199, -1, 2942, -1, 2339, -1, 5124, -1], 'generators': [1675405, 887131, 622105, 835777, 70633, 793169, 767155], 'label': '1728.46354.6.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1.a1', 'old_label': '6.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.be1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336480
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.d1.a1', '108.h1.a1', '108.j1.a1', '108.q1.a1', '108.u1.a1', '108.bj1.a1', '108.bk1.a1', '108.bl1.a1', '108.bm1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1027, -1, 7632, -1, 7464, -1, 7482, -1], 'generators': [46999, 1674451, 835777, 887131], 'label': '1728.46354.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336481
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.f1.a1', '108.i1.a1', '108.k1.a1', '108.t1.a1', '108.v1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3502, -1, 8259, -1, 6133, -1, 6731, -1], 'generators': [46999, 1674451, 811801], 'label': '1728.46354.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336482
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.e1.a1', '108.f1.a1', '108.r1.a1', '108.s1.a1', '108.z1.a1', '108.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4199, -1, 6567, -1, 5648, -1, 6298, -1], 'generators': [70957, 1674451, 835777], 'label': '1728.46354.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336483
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.h1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.d1.a1', '108.e1.a1', '108.w1.a1', '108.x1.a1', '108.y1.a1', '108.bb1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1597, -1, 6309, -1, 5712, -1, 6326, -1], 'generators': [70957, 1674451, 811801], 'label': '1728.46354.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336484
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.k1.a1', '27.a1.a1'], 'contains': ['108.g1.a1', '108.h1.a1', '108.k1.a1', '108.l1.a1', '108.o1.a1', '108.s1.a1', '108.y1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2822, -1, 8491, -1, 5944, -1, 6457, -1], 'generators': [46999, 1651771, 811801], 'label': '1728.46354.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336485
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.l1.a1', '27.a1.a1'], 'contains': ['108.g1.a1', '108.i1.a1', '108.j1.a1', '108.n1.a1', '108.p1.a1', '108.x1.a1', '108.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [841, -1, 5981, -1, 5682, -1, 6424, -1], 'generators': [46999, 1651771, 835777], 'label': '1728.46354.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336486
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.o1.a1', '27.a1.a1'], 'contains': ['108.l1.a1', '108.m1.a1', '108.p1.a1', '108.q1.a1', '108.r1.a1', '108.v1.a1', '108.bb1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2299, -1, 7037, -1, 5836, -1, 6352, -1], 'generators': [70957, 1651771, 811801], 'label': '1728.46354.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336487
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '18.p1.a1', '27.a1.a1'], 'contains': ['108.m1.a1', '108.n1.a1', '108.o1.a1', '108.t1.a1', '108.u1.a1', '108.w1.a1', '108.z1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1944, -1, 7412, -1, 6004, -1, 6602, -1], 'generators': [70957, 1651771, 835777], 'label': '1728.46354.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336488
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '18.r1.a1', '18.x1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '108.g1.a1', '108.m1.a1', '108.bc1.a1', '108.bd1.a1', '108.bf1.a1', '108.bn1.a1', '108.bn1.b1', '108.bp1.a1', '108.bp1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6148, -1, 5230, -1, 4763, -1, 4876, -1], 'generators': [46999, 1674451, 793169, 70633], 'label': '1728.46354.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336489
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.t1.a1', '18.y1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1', '108.l1.a1', '108.n1.a1', '108.bc1.a1', '108.be1.a1', '108.bh1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4026, -1, 5935, -1, 5108, -1, 5880, -1], 'generators': [1674451, 835777, 887131, 70633], 'label': '1728.46354.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336490
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '6.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 12, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.c1.a1'], 'contains': ['12.f1.a1', '12.by1.a1', '12.ce1.a1', '18.bl1.a1', '18.bm1.a1', '18.bn1.a1', '24.ce1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6816, -1, 3541, -1, 2385, -1, 4148, -1], 'generators': [1675405, 887131, 622537, 835777, 70633, 793169, 1341703], 'label': '1728.46354.6.bf1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336491
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1.a1', '18.v1.a1', '18.w1.a1', '18.z1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.f1.a1', '108.o1.a1', '108.p1.a1', '108.bc1.a1', '108.bg1.a1', '108.bi1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4899, -1, 5474, -1, 4325, -1, 5335, -1], 'generators': [834823, 1674451, 70633], 'label': '1728.46354.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336492
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ba1.a1', '18.bb1.a1', '18.bc1.a1', '18.bf1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '108.i1.a1', '108.r1.a1', '108.w1.a1', '108.bd1.a1', '108.be1.a1', '108.bg1.a1', '108.bo1.a1', '108.bo1.b1', '108.bq1.a1', '108.bq1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5655, -1, 3699, -1, 3853, -1, 3775, -1], 'generators': [46999, 1634131, 793169, 70633], 'label': '1728.46354.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336493
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bd1.a1', '18.be1.a1', '18.bg1.a1', '27.a1.a1'], 'contains': ['108.j1.a1', '108.k1.a1', '108.z1.a1', '108.bb1.a1', '108.bd1.a1', '108.bh1.a1', '108.bi1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3441, -1, 5912, -1, 5069, -1, 5680, -1], 'generators': [46999, 835777, 70633], 'label': '1728.46354.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336494
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bh1.a1', '18.bi1.a1', '18.bj1.a1', '27.a1.a1'], 'contains': ['108.q1.a1', '108.s1.a1', '108.t1.a1', '108.x1.a1', '108.be1.a1', '108.bf1.a1', '108.bi1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4850, -1, 5883, -1, 5027, -1, 5645, -1], 'generators': [834823, 1634131, 70633], 'label': '1728.46354.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336495
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1.a1', '18.bl1.a1', '18.bm1.a1', '18.bn1.a1', '27.a1.a1'], 'contains': ['108.u1.a1', '108.v1.a1', '108.y1.a1', '108.ba1.a1', '108.bf1.a1', '108.bg1.a1', '108.bh1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5682, -1, 5769, -1, 4938, -1, 5708, -1], 'generators': [1675405, 835777, 70633], 'label': '1728.46354.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336496
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.a1.a1', '32.b1.a1', '32.c1.a1', '32.c1.b1', '32.d1.a1', '32.e1.a1', '32.f1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '192.d1.a1', '192.e1.a1', '192.f1.a1', '192.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9759, -1, 666, -1, 1167, -1, 1052, -1], 'generators': [1341703, 622537, 622105], 'label': '1728.46354.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336497
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.u1.a1', '36.c1.a1', '36.cl1.a1', '36.co1.a1', '36.cs1.a1', '36.cv1.a1', '36.cz1.a1', '36.dg1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.cm1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5268, 4303, 5417, 4918, 4106, 4782, 4605, 4135], 'generators': [793169, 887131, 70633, 622105], 'label': '1728.46354.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.c1.a1'], 'normal_contains': ['144.c1.a1', '216.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336498
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '72.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.c1.a1', '24.v1.a1', '36.a1.a1', '36.cp1.a1', '36.ct1.a1', '36.cw1.a1', '36.da1.a1', '36.dh1.a1', '36.di1.a1'], 'contains': ['144.d1.a1', '144.g1.a1', '144.cn1.a1', '216.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5299, 6390, 5611, 3785, 3815, 5940, 4801, 4841], 'generators': [793169, 887131, 70633, 622537], 'label': '1728.46354.72.b1.a1', 'mobius_quo': -1, 'mobius_sub': -72, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '24.c1.a1', '36.a1.a1'], 'normal_contains': ['144.d1.a1', '216.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336499
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.w1.a1', '36.b1.a1', '36.cm1.a1', '36.cr1.a1', '36.cx1.a1', '36.dc1.a1', '36.dj1.a1', '36.dk1.a1'], 'contains': ['144.e1.a1', '216.a1.a1', '288.d1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7378, 2610, 2816, 6551, 1474, 3426, 1396, 5939], 'generators': [793169, 1341703, 887131, 70633], 'label': '1728.46354.72.c1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.b1.a1', '24.c1.a1', '36.b1.a1'], 'normal_contains': ['144.e1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336500
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '24.d1.a1', 'complements': ['24.d1.a1', '24.bt1.a1', '24.be1.a1', '24.bs1.a1', '24.bu1.a1', '24.ca1.a1', '24.cb1.a1', '24.cd1.a1', '24.bf1.a1', '24.ch1.a1', '24.bv1.a1', '24.bh1.a1', '24.by1.a1', '24.bz1.a1', '24.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.db1.a1', '36.b1.a1', '36.ec1.a1', '36.eh1.a1'], 'contains': ['144.e1.a1', '216.by1.a1', '288.u1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9241, 1268, 801, 7586, 982, 2171, 383, 8768], 'generators': [46999, 1341703, 887131, 70633], 'label': '1728.46354.72.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': ['24.e1.a1', '24.f1.a1', '36.b1.a1'], 'normal_contains': ['144.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336501
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '32.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7712, 4383, 2445, 5523, 1258, 4468, 1577, 4464], 'generators': [793169, 70633, 887131, 1341703, 622537, 622105], 'label': '1728.46354.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336516
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.f1.a1', '36.u1.a1', '36.bd1.a1', '36.bs1.a1', '36.by1.a1', '36.cb1.a1', '36.cs1.a1'], 'contains': ['144.f1.a1', '144.z1.a1', '144.ce1.a1', '144.db1.a1', '216.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2779, -1, 6589, -1, 7326, -1, 6761, -1], 'generators': [1656811, 793169, 887131, 622105], 'label': '1728.46354.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336502
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '24.d1.a1', 'complements': ['24.d1.a1', '24.bt1.a1', '24.be1.a1', '24.bs1.a1', '24.bu1.a1', '24.ca1.a1', '24.cb1.a1', '24.cd1.a1', '24.bf1.a1', '24.ch1.a1', '24.bv1.a1', '24.bh1.a1', '24.by1.a1', '24.bz1.a1', '24.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.db1.b1', '36.b1.a1', '36.ec1.b1', '36.eh1.b1'], 'contains': ['144.e1.a1', '216.by1.b1', '288.u1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9241, 1268, 837, 7054, 982, 2171, 485, 7765], 'generators': [793511, 1341703, 887131, 70633], 'label': '1728.46354.72.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.d1.b1', 'normal_contained_in': ['24.e1.b1', '24.f1.b1', '36.b1.a1'], 'normal_contains': ['144.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.b1', 'projective_image': '1728.46354', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336503
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.i1.a1', '36.cl1.a1'], 'contains': ['144.f1.a1', '144.i1.a1', '144.p1.a1', '144.bs1.a1', '144.cp1.a1', '216.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3680, -1, 7922, -1, 7963, -1, 7143, -1], 'generators': [1674451, 793169, 887131, 622105], 'label': '1728.46354.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336504
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.a1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1'], 'contains': ['144.a1.a1', '144.g1.a1', '144.q1.a1', '144.bt1.a1', '144.cq1.a1', '216.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4135, -1, 7737, -1, 6862, -1, 8187, -1], 'generators': [1674451, 793169, 887131, 622537], 'label': '1728.46354.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336505
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.d1.a1', '36.p1.a1', '36.r1.a1', '36.u1.a1', '36.x1.a1', '36.y1.a1', '36.co1.a1'], 'contains': ['144.f1.a1', '144.l1.a1', '144.bu1.a1', '144.cr1.a1', '144.cr1.b1', '216.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2165, -1, 7043, -1, 7831, -1, 6967, -1], 'generators': [46999, 793169, 887131, 622105], 'label': '1728.46354.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336506
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.j1.a1', '36.q1.a1', '36.s1.a1', '36.v1.a1', '36.z1.a1', '36.ba1.a1', '36.cp1.a1'], 'contains': ['144.g1.a1', '144.m1.a1', '144.bv1.a1', '144.cs1.a1', '144.cs1.b1', '216.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2134, -1, 6958, -1, 6733, -1, 7951, -1], 'generators': [46999, 793169, 887131, 622537], 'label': '1728.46354.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336507
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.t1.a1', '36.w1.a1', '36.cq1.a1'], 'contains': ['144.h1.a1', '144.n1.a1', '144.bw1.a1', '144.ct1.a1', '144.ct1.b1', '216.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5055, -1, 5107, -1, 5246, -1, 5431, -1], 'generators': [46999, 793169, 887131, 47089], 'label': '1728.46354.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336508
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.p1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.be1.a1', '36.bf1.a1', '36.cl1.a1'], 'contains': ['144.f1.a1', '144.p1.a1', '144.bx1.a1', '144.cu1.a1', '216.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [938, -1, 6476, -1, 7550, -1, 6726, -1], 'generators': [1651771, 793169, 887131, 622105], 'label': '1728.46354.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336509
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.a1.a1', '36.q1.a1', '36.bg1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1', '36.bk1.a1'], 'contains': ['144.g1.a1', '144.q1.a1', '144.by1.a1', '144.cv1.a1', '216.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1688, -1, 6295, -1, 6147, -1, 7694, -1], 'generators': [1651771, 793169, 887131, 622537], 'label': '1728.46354.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336510
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.e1.a1', '36.r1.a1', '36.bb1.a1', '36.bl1.a1', '36.bn1.a1', '36.bo1.a1', '36.cs1.a1'], 'contains': ['144.f1.a1', '144.s1.a1', '144.z1.a1', '144.bz1.a1', '144.cw1.a1', '216.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3773, -1, 8587, -1, 7789, -1, 7070, -1], 'generators': [1634131, 793169, 887131, 622105], 'label': '1728.46354.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336511
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.k1.a1', '36.s1.a1', '36.bg1.a1', '36.bm1.a1', '36.bp1.a1', '36.bq1.a1', '36.ct1.a1'], 'contains': ['144.g1.a1', '144.t1.a1', '144.ba1.a1', '144.ca1.a1', '144.cx1.a1', '216.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4300, -1, 7829, -1, 6691, -1, 8078, -1], 'generators': [1634131, 793169, 887131, 622537], 'label': '1728.46354.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336512
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['216.q1.a1', '216.z1.a1', '216.r1.a1', '216.y1.a1', '216.ba1.a1', '216.be1.a1', '216.bf1.a1', '216.s1.a1', '216.bi1.a1', '216.bb1.a1', '216.bc1.a1', '216.bd1.a1', '216.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '24.e1.a1', '24.f1.a1', '24.da1.a1', '24.db1.a1', '32.c1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9453, 1041, 1070, 8773, 956, 1279, 946, 9690], 'generators': [46999, 70633, 887131, 622537, 622105, 1341703], 'label': '1728.46354.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336513
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.t1.a1', '36.br1.a1', '36.cu1.a1'], 'contains': ['144.h1.a1', '144.u1.a1', '144.bb1.a1', '144.cb1.a1', '144.cb1.a2', '144.cy1.a1', '144.cy1.a2', '216.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5482, -1, 5305, -1, 5204, -1, 5496, -1], 'generators': [1634131, 793169, 887131, 47089], 'label': '1728.46354.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336514
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.d1.a1', '36.bc1.a1', '36.bl1.a1', '36.bs1.a1', '36.bt1.a1', '36.bu1.a1', '36.cv1.a1'], 'contains': ['144.f1.a1', '144.v1.a1', '144.cc1.a1', '144.cz1.a1', '216.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2475, -1, 8426, -1, 8094, -1, 7178, -1], 'generators': [1675405, 793169, 887131, 622105], 'label': '1728.46354.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336515
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.j1.a1', '36.bh1.a1', '36.bm1.a1', '36.bv1.a1', '36.bw1.a1', '36.bx1.a1', '36.cw1.a1'], 'contains': ['144.g1.a1', '144.w1.a1', '144.cd1.a1', '144.da1.a1', '216.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3010, -1, 7883, -1, 6941, -1, 8222, -1], 'generators': [1675405, 793169, 887131, 622537], 'label': '1728.46354.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336517
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.l1.a1', '36.v1.a1', '36.bi1.a1', '36.bv1.a1', '36.bz1.a1', '36.cc1.a1', '36.ct1.a1'], 'contains': ['144.g1.a1', '144.ba1.a1', '144.cf1.a1', '144.dc1.a1', '216.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3123, -1, 6243, -1, 6068, -1, 7659, -1], 'generators': [1656811, 793169, 887131, 622537], 'label': '1728.46354.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336518
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.w1.a1', '36.ca1.a1', '36.cu1.a1'], 'contains': ['144.h1.a1', '144.bb1.a1', '144.cg1.a1', '144.dd1.a1', '144.dd1.a2', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4985, -1, 4254, -1, 5011, -1, 5310, -1], 'generators': [1656811, 793169, 887131, 47089], 'label': '1728.46354.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336519
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.g1.a1', '36.r1.a1', '36.be1.a1', '36.bt1.a1', '36.by1.a1', '36.cd1.a1', '36.cz1.a1'], 'contains': ['144.f1.a1', '144.bc1.a1', '144.ch1.a1', '144.de1.a1', '216.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [984, -1, 8029, -1, 7703, -1, 6932, -1], 'generators': [1633789, 793169, 887131, 622105], 'label': '1728.46354.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336520
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.m1.a1', '36.s1.a1', '36.bj1.a1', '36.bw1.a1', '36.bz1.a1', '36.ce1.a1', '36.da1.a1'], 'contains': ['144.g1.a1', '144.bd1.a1', '144.ci1.a1', '144.df1.a1', '216.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1752, -1, 7555, -1, 6627, -1, 7915, -1], 'generators': [1633789, 793169, 887131, 622537], 'label': '1728.46354.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336521
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.t1.a1', '36.ca1.a1', '36.db1.a1'], 'contains': ['144.h1.a1', '144.be1.a1', '144.cj1.a1', '144.dg1.a1', '144.dg1.a2', '216.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4955, -1, 5132, -1, 5162, -1, 5396, -1], 'generators': [1633789, 793169, 887131, 47089], 'label': '1728.46354.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336522
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.c1.a1', '36.e1.a1', '36.x1.a1', '36.bd1.a1', '36.bt1.a1', '36.cf1.a1', '36.cg1.a1'], 'contains': ['144.b1.a1', '144.f1.a1', '144.bj1.a1', '216.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [774, -1, 7017, -1, 7920, -1, 7329, -1], 'generators': [835777, 887131, 793169, 622105], 'label': '1728.46354.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336523
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['216.q1.a1', '216.z1.a1', '216.r1.a1', '216.y1.a1', '216.ba1.a1', '216.be1.a1', '216.bf1.a1', '216.s1.a1', '216.bi1.a1', '216.bb1.a1', '216.bc1.a1', '216.bd1.a1', '216.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.b1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.e1.b1', '24.f1.b1', '24.da1.b1', '24.db1.b1', '32.c1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9453, 1041, 1095, 7364, 956, 1279, 1156, 7769], 'generators': [793511, 70633, 887131, 622537, 622105, 1341703], 'label': '1728.46354.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.b1', '24.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '1728.46354', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336524
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.h1.a1', '36.bc1.a1', '36.bn1.a1', '36.by1.a1', '36.cf1.a1', '36.ch1.a1', '36.co1.a1'], 'contains': ['144.f1.a1', '144.dh1.a1', '144.dh1.b1', '216.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1130, -1, 7359, -1, 6454, -1, 6130, -1], 'generators': [70957, 793169, 622105, 887131], 'label': '1728.46354.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336525
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.c1.a1', '36.f1.a1', '36.y1.a1', '36.bb1.a1', '36.bu1.a1', '36.cd1.a1', '36.ch1.a1'], 'contains': ['144.f1.a1', '144.bj1.a1', '216.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1792, -1, 8181, -1, 7638, -1, 7034, -1], 'generators': [811801, 887131, 793169, 622105], 'label': '1728.46354.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336526
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.g1.a1', '36.x1.a1', '36.bf1.a1', '36.bl1.a1', '36.cb1.a1', '36.ch1.a1', '36.dg1.a1'], 'contains': ['144.f1.a1', '144.bk1.a1', '216.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [561, -1, 6926, -1, 7875, -1, 7107, -1], 'generators': [834823, 887131, 793169, 622105], 'label': '1728.46354.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336527
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.h1.a1', '36.p1.a1', '36.bo1.a1', '36.cb1.a1', '36.cd1.a1', '36.cg1.a1', '36.cv1.a1'], 'contains': ['144.f1.a1', '144.di1.a1', '216.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4268, -1, 6425, -1, 6498, -1, 6378, -1], 'generators': [1651447, 793169, 622105, 887131], 'label': '1728.46354.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336528
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.i1.a1', '36.y1.a1', '36.be1.a1', '36.bo1.a1', '36.bs1.a1', '36.cf1.a1', '36.dg1.a1'], 'contains': ['144.f1.a1', '144.ck1.a1', '216.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2619, -1, 8798, -1, 7593, -1, 6859, -1], 'generators': [812125, 887131, 1633643, 622105], 'label': '1728.46354.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336529
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.i1.a1', '36.u1.a1', '36.bf1.a1', '36.bn1.a1', '36.bu1.a1', '36.cg1.a1', '36.cz1.a1'], 'contains': ['144.f1.a1', '144.dj1.a1', '216.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4103, -1, 6356, -1, 6542, -1, 6202, -1], 'generators': [1656487, 793169, 887131, 622105], 'label': '1728.46354.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336530
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.k1.a1', '36.z1.a1', '36.bi1.a1', '36.bw1.a1', '36.ci1.a1', '36.cj1.a1', '36.dh1.a1'], 'contains': ['144.g1.a1', '144.bl1.a1', '144.bm1.a1', '216.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1367, -1, 6857, -1, 6819, -1, 8258, -1], 'generators': [835777, 887131, 622537, 793169], 'label': '1728.46354.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336531
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '12.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.n1.a1', '36.bh1.a1', '36.bp1.a1', '36.bz1.a1', '36.ci1.a1', '36.ck1.a1', '36.cp1.a1'], 'contains': ['144.g1.a1', '144.dk1.a1', '144.dk1.b1', '216.j1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2259, -1, 6717, -1, 5530, -1, 6239, -1], 'generators': [70957, 793169, 622537, 887131], 'label': '1728.46354.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336532
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.l1.a1', '36.ba1.a1', '36.bg1.a1', '36.bx1.a1', '36.ce1.a1', '36.ck1.a1', '36.dh1.a1'], 'contains': ['144.g1.a1', '144.bm1.a1', '216.k1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2299, -1, 7980, -1, 6330, -1, 7880, -1], 'generators': [811801, 887131, 622537, 793169], 'label': '1728.46354.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336533
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.m1.a1', '36.z1.a1', '36.bk1.a1', '36.bm1.a1', '36.cc1.a1', '36.ck1.a1', '36.di1.a1'], 'contains': ['144.g1.a1', '144.bn1.a1', '216.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1185, -1, 6673, -1, 6776, -1, 8151, -1], 'generators': [834823, 887131, 622537, 793169], 'label': '1728.46354.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336534
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1', '16.i1.a1', '16.i1.b1', '24.y1.a1', '24.bb1.a1', '24.bc1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7982, -1, 3182, -1, 2293, -1, 2410, -1], 'generators': [46999, 622537, 1341703, 1674451, 793169, 622105], 'label': '1728.46354.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.c1.a1', 'projective_image': '864.4673', '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': '72.46'}
  • id: 264336535
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.n1.a1', '36.q1.a1', '36.bq1.a1', '36.cc1.a1', '36.ce1.a1', '36.cj1.a1', '36.cw1.a1'], 'contains': ['144.g1.a1', '144.dl1.a1', '216.m1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4413, -1, 6121, -1, 5653, -1, 6896, -1], 'generators': [1651447, 793169, 887131, 622537], 'label': '1728.46354.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336536
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.o1.a1', '36.ba1.a1', '36.bj1.a1', '36.bq1.a1', '36.bv1.a1', '36.ci1.a1', '36.di1.a1'], 'contains': ['144.g1.a1', '144.cl1.a1', '216.n1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2889, -1, 8382, -1, 6374, -1, 7843, -1], 'generators': [812125, 887131, 622537, 1633643], 'label': '1728.46354.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336537
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.o1.a1', '36.v1.a1', '36.bk1.a1', '36.bp1.a1', '36.bx1.a1', '36.cj1.a1', '36.da1.a1'], 'contains': ['144.g1.a1', '144.dm1.a1', '216.o1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4460, -1, 6153, -1, 5697, -1, 6509, -1], 'generators': [1656487, 793169, 887131, 622537], 'label': '1728.46354.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336538
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.br1.a1', '36.ca1.a1', '36.cq1.a1'], 'contains': ['144.h1.a1', '144.dn1.a1', '144.dn1.b1', '216.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5513, -1, 4717, -1, 4839, -1, 4640, -1], 'generators': [70957, 793169, 47089, 887131], 'label': '1728.46354.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336539
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.w1.a1', '36.br1.a1', '36.db1.a1'], 'contains': ['144.h1.a1', '144.do1.a1', '144.do1.a2', '216.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5659, -1, 4679, -1, 4884, -1, 4677, -1], 'generators': [1656487, 793169, 887131, 47089], 'label': '1728.46354.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336540
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.w1.a1', '24.x1.a1', '36.cq1.a1', '36.cu1.a1', '36.db1.a1'], 'contains': ['144.h1.a1', '144.co1.a1', '144.dp1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8404, -1, 1412, -1, 2942, -1, 2336, -1], 'generators': [793169, 887131, 70633, 47089], 'label': '1728.46354.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '72.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336541
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.v1.a1', '24.x1.a1', '36.cn1.a1', '36.dd1.a1', '36.dl1.a1'], 'contains': ['144.dq1.a1', '216.a1.a1', '288.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8080, -1, 1184, -1, 382, -1, 508, -1], 'generators': [793169, 766291, 887131, 70633], 'label': '1728.46354.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336542
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.u1.a1', '24.x1.a1', '36.cy1.a1', '36.de1.a1', '36.dm1.a1'], 'contains': ['144.dr1.a1', '216.a1.a1', '288.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8635, -1, 1953, -1, 1175, -1, 1996, -1], 'generators': [793169, 767155, 887131, 70633], 'label': '1728.46354.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '72.bo1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336543
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '36.df1.a1'], 'contains': ['144.ds1.a1', '216.a1.a1', '288.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8841, -1, 1034, -1, 243, -1, 325, -1], 'generators': [793169, 1342135, 887131, 70633], 'label': '1728.46354.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '72.bp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336544
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bb1.a1', '36.d1.a1', '36.dn1.a1', '36.do1.a1'], 'contains': ['144.i1.a1', '144.l1.a1', '144.v1.a1', '144.dt1.a1', '144.dt1.b1', '216.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3852, -1, 8618, -1, 9431, -1, 7787, -1], 'generators': [46999, 1674451, 793169, 622105], 'label': '1728.46354.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336545
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 6, 'centralizer': '288.b1.a1', 'complements': ['864.d1.a1', '864.f1.a1', '864.h1.a1', '864.g1.a1', '864.i1.a1', '864.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.f1.a1', '4.g1.a1', '6.c1.a1', '6.u1.a1', '6.y1.a1', '8.g1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4695, 1188, 5637, 8018, 2761, 1689, 3470, 6078], 'generators': [46999, 1341703, 622105, 835777, 793169, 70633, 887131, 622537], 'label': '1728.46354.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.f1.a1', '4.g1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '864.4673', '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': '288.1028'}
  • id: 264336546
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.g1.a1', '24.d1.a1', '24.z1.a1', '24.bd1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5044, -1, 4332, -1, 2176, -1, 3329, -1], 'generators': [1674451, 622105, 622537, 835777, 1341703, 793169], 'label': '1728.46354.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336547
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1', '24.y1.a1', '24.bc1.a1', '36.dp1.a1'], 'contains': ['144.j1.a1', '144.o1.a1', '144.x1.a1', '144.du1.a1', '144.du1.b1', '216.p1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7640, -1, 2876, -1, 2093, -1, 1909, -1], 'generators': [46999, 1674451, 793169, 1341703], 'label': '1728.46354.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '72.br1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336548
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '24.z1.a1', '24.bd1.a1', '36.dp1.a1'], 'contains': ['144.j1.a1', '144.r1.a1', '144.bo1.a1', '216.q1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5100, -1, 4212, -1, 2213, -1, 3355, -1], 'generators': [1674451, 835777, 1341703, 793169], 'label': '1728.46354.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '72.bs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336549
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.z1.a1', '36.e1.a1', '36.dn1.a1'], 'contains': ['144.b1.a1', '144.i1.a1', '144.s1.a1', '216.q1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4501, -1, 6996, -1, 7492, -1, 7455, -1], 'generators': [1674451, 835777, 793169, 622105], 'label': '1728.46354.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bt1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336550
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.e1.a1', '36.f1.a1', '36.do1.a1'], 'contains': ['144.i1.a1', '144.z1.a1', '144.bj1.a1', '216.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3197, -1, 8336, -1, 9397, -1, 8385, -1], 'generators': [1674451, 1674955, 793169, 622105], 'label': '1728.46354.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336551
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bf1.a1', '36.g1.a1', '36.dn1.a1', '36.do1.a1'], 'contains': ['144.i1.a1', '144.bc1.a1', '144.bk1.a1', '216.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [463, -1, 7616, -1, 8478, -1, 7506, -1], 'generators': [834823, 1674451, 793169, 622105], 'label': '1728.46354.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336552
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1.a1', '24.ba1.a1', '24.bg1.a1', '36.dp1.a1'], 'contains': ['144.j1.a1', '144.bf1.a1', '144.bp1.a1', '216.s1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5603, -1, 3208, -1, 1995, -1, 2162, -1], 'generators': [834823, 1674451, 793169, 1341703], 'label': '1728.46354.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '72.bw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336553
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1.a1', '24.ba1.a1', '24.bh1.a1'], 'contains': ['144.k1.a1', '144.bg1.a1', '144.bq1.a1', '216.s1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7546, -1, 2205, -1, 883, -1, 1117, -1], 'generators': [834823, 1674451, 793169, 766291], 'label': '1728.46354.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bx1.a1', 'old_label': '72.bx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336554
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '24.bc1.a1', '36.j1.a1', '36.dq1.a1', '36.dr1.a1'], 'contains': ['144.a1.a1', '144.m1.a1', '144.w1.a1', '144.dv1.a1', '144.dv1.b1', '216.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4167, -1, 8537, -1, 7459, -1, 9378, -1], 'generators': [46999, 1674451, 793169, 622537], 'label': '1728.46354.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.by1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336555
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.bd1.a1', '36.k1.a1', '36.dq1.a1'], 'contains': ['144.a1.a1', '144.t1.a1', '144.bl1.a1', '216.q1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4534, -1, 7133, -1, 7149, -1, 8364, -1], 'generators': [1674451, 835777, 793169, 622537], 'label': '1728.46354.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.bz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336556
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.k1.a1', '36.l1.a1', '36.dr1.a1'], 'contains': ['144.a1.a1', '144.ba1.a1', '144.bm1.a1', '216.r1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3314, -1, 8704, -1, 8196, -1, 9313, -1], 'generators': [1674451, 1674955, 793169, 622537], 'label': '1728.46354.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.ca1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336557
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.h1.a1', '24.ba1.a1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6875, -1, 3487, -1, 1902, -1, 2325, -1], 'generators': [834823, 622105, 622537, 1674451, 793169, 1341703], 'label': '1728.46354.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336558
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bg1.a1', '24.bh1.a1', '36.m1.a1', '36.dq1.a1', '36.dr1.a1'], 'contains': ['144.a1.a1', '144.bd1.a1', '144.bn1.a1', '216.s1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2003, -1, 7314, -1, 7214, -1, 8574, -1], 'generators': [834823, 1674451, 793169, 622537], 'label': '1728.46354.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.cb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336559
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.d1.a1', '36.ds1.a1', '36.dt1.a1'], 'contains': ['144.l1.a1', '144.p1.a1', '144.v1.a1', '144.dw1.a1', '144.dw1.b1', '216.t1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [226, -1, 9679, -1, 9903, -1, 8969, -1], 'generators': [46999, 835273, 793169, 622105], 'label': '1728.46354.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336560
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.j1.a1', '36.du1.a1', '36.dv1.a1'], 'contains': ['144.m1.a1', '144.q1.a1', '144.w1.a1', '144.dx1.a1', '144.dx1.b1', '216.t1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [430, -1, 9217, -1, 9052, -1, 9859, -1], 'generators': [46999, 835273, 793169, 622537], 'label': '1728.46354.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.cd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336561
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '24.bn1.a1', '36.r1.a1', '36.dn1.a1', '36.ds1.a1'], 'contains': ['144.l1.a1', '144.s1.a1', '144.bc1.a1', '144.dy1.a1', '144.dy1.b1', '216.u1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3483, -1, 8872, -1, 8295, -1, 7427, -1], 'generators': [46999, 1634131, 793169, 622105], 'label': '1728.46354.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ce1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336562
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '24.bo1.a1', '36.s1.a1', '36.dq1.a1', '36.du1.a1'], 'contains': ['144.m1.a1', '144.t1.a1', '144.bd1.a1', '144.dz1.a1', '144.dz1.b1', '216.u1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3537, -1, 8561, -1, 7181, -1, 8547, -1], 'generators': [46999, 1634131, 793169, 622537], 'label': '1728.46354.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.cf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336563
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '24.bp1.a1', '36.t1.a1'], 'contains': ['144.n1.a1', '144.u1.a1', '144.be1.a1', '144.ea1.a1', '144.ea1.a2', '144.ea1.b1', '144.ea1.b2', '216.u1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5016, -1, 5519, -1, 5408, -1, 5998, -1], 'generators': [46999, 1634131, 793169, 47089], 'label': '1728.46354.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '72.cg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336564
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.r1.a1', '36.do1.a1', '36.dt1.a1'], 'contains': ['144.l1.a1', '144.z1.a1', '144.bc1.a1', '144.eb1.a1', '144.eb1.b1', '216.v1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [257, -1, 9598, -1, 9614, -1, 8768, -1], 'generators': [46999, 793657, 793169, 622105], 'label': '1728.46354.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ch1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336565
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.s1.a1', '36.dr1.a1', '36.dv1.a1'], 'contains': ['144.m1.a1', '144.ba1.a1', '144.bd1.a1', '144.ec1.a1', '144.ec1.b1', '216.v1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [697, -1, 9186, -1, 8673, -1, 9652, -1], 'generators': [46999, 793657, 793169, 622537], 'label': '1728.46354.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.ci1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336566
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.t1.a1'], 'contains': ['144.n1.a1', '144.bb1.a1', '144.be1.a1', '144.ed1.a1', '144.ed1.a2', '144.ed1.b1', '144.ed1.b2', '216.v1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2513, -1, 7667, -1, 6585, -1, 7554, -1], 'generators': [46999, 793657, 793169, 47089], 'label': '1728.46354.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '72.cj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336567
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.bq1.a1', '36.x1.a1', '36.dn1.a1', '36.dt1.a1'], 'contains': ['144.b1.a1', '144.l1.a1', '144.bk1.a1', '216.w1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [349, -1, 7101, -1, 8537, -1, 7750, -1], 'generators': [46999, 835777, 793169, 622105], 'label': '1728.46354.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.ck1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336568
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.h1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.f1.a1', '16.j1.a1', '16.j1.b1', '24.bj1.a1', '24.bn1.a1', '24.bo1.a1', '24.bp1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7569, -1, 2622, -1, 1600, -1, 1797, -1], 'generators': [46999, 622105, 622537, 1634131, 793169, 1341703], 'label': '1728.46354.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336569
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.x1.a1', '36.do1.a1', '36.ds1.a1'], 'contains': ['144.l1.a1', '144.bj1.a1', '144.bk1.a1', '216.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [135, -1, 9524, -1, 9658, -1, 8469, -1], 'generators': [46999, 1674955, 793169, 622105], 'label': '1728.46354.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.cl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336570
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.br1.a1', '36.z1.a1', '36.dq1.a1', '36.dv1.a1'], 'contains': ['144.m1.a1', '144.bl1.a1', '144.bn1.a1', '216.w1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [640, -1, 7075, -1, 7393, -1, 9062, -1], 'generators': [46999, 835777, 622537, 793169], 'label': '1728.46354.72.cm1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.cm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336571
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.z1.a1', '36.dr1.a1', '36.du1.a1'], 'contains': ['144.m1.a1', '144.bm1.a1', '144.bn1.a1', '216.x1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [399, -1, 9111, -1, 8606, -1, 9687, -1], 'generators': [46999, 1674955, 622537, 793169], 'label': '1728.46354.72.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.cn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336572
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1.a1', '24.bn1.a1', '24.bo1.a1', '24.bp1.a1', '36.dp1.a1'], 'contains': ['144.o1.a1', '144.r1.a1', '144.bf1.a1', '144.ee1.a1', '144.ee1.b1', '216.u1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7594, -1, 1917, -1, 1621, -1, 1288, -1], 'generators': [46999, 1634131, 793169, 1341703], 'label': '1728.46354.72.co1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '72.co1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336573
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bg1.a1', '24.bq1.a1', '24.br1.a1', '36.dp1.a1'], 'contains': ['144.o1.a1', '144.bo1.a1', '144.bp1.a1', '216.w1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4823, -1, 5715, -1, 2498, -1, 3386, -1], 'generators': [46999, 835777, 793169, 1341703], 'label': '1728.46354.72.cp1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '72.cp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336574
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '36.e1.a1', '36.bb1.a1', '36.ds1.a1'], 'contains': ['144.p1.a1', '144.s1.a1', '144.bj1.a1', '216.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1319, -1, 9138, -1, 9303, -1, 8286, -1], 'generators': [835273, 1674955, 793169, 622105], 'label': '1728.46354.72.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336575
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '36.e1.a1', '36.bd1.a1', '36.dt1.a1'], 'contains': ['144.b1.a1', '144.p1.a1', '144.z1.a1', '216.z1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [315, -1, 8891, -1, 9327, -1, 8307, -1], 'generators': [835273, 835777, 793169, 622105], 'label': '1728.46354.72.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cr1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336576
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '36.f1.a1', '36.bb1.a1', '36.bd1.a1'], 'contains': ['144.p1.a1', '144.z1.a1', '144.bj1.a1', '216.ba1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1274, -1, 8680, -1, 8832, -1, 7815, -1], 'generators': [1651771, 1674955, 793169, 622105], 'label': '1728.46354.72.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.a1', 'old_label': '72.cs1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336577
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '36.g1.a1', '36.ds1.a1', '36.dt1.a1'], 'contains': ['144.p1.a1', '144.bc1.a1', '144.bk1.a1', '216.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [90, -1, 9482, -1, 9581, -1, 8405, -1], 'generators': [834823, 835273, 793169, 622105], 'label': '1728.46354.72.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ct1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336578
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '36.k1.a1', '36.bg1.a1', '36.du1.a1'], 'contains': ['144.q1.a1', '144.t1.a1', '144.bm1.a1', '216.y1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1865, -1, 9062, -1, 8127, -1, 9294, -1], 'generators': [835273, 1674955, 793169, 622537], 'label': '1728.46354.72.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.cu1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336579
    {'ambient': '1728.46354', 'aut_centralizer_order': 6, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.h1.a1'], 'contains': ['16.c1.a1', '16.g1.a1', '16.h1.a1', '24.bl1.a1', '24.bq1.a1', '24.br1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4743, -1, 5675, -1, 2956, -1, 3575, -1], 'generators': [46999, 622105, 1341703, 835777, 622537, 793169], 'label': '1728.46354.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336580
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '36.k1.a1', '36.bi1.a1', '36.dv1.a1'], 'contains': ['144.q1.a1', '144.ba1.a1', '144.bl1.a1', '216.z1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [506, -1, 8906, -1, 8262, -1, 9274, -1], 'generators': [835273, 835777, 793169, 622537], 'label': '1728.46354.72.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '72.cv1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336581
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '36.l1.a1', '36.bg1.a1', '36.bi1.a1'], 'contains': ['144.q1.a1', '144.ba1.a1', '144.bm1.a1', '216.ba1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1832, -1, 8350, -1, 7517, -1, 8673, -1], 'generators': [1651771, 1674955, 793169, 622537], 'label': '1728.46354.72.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '72.cw1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336582
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '36.m1.a1', '36.du1.a1', '36.dv1.a1'], 'contains': ['144.q1.a1', '144.bd1.a1', '144.bn1.a1', '216.bb1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [374, -1, 9076, -1, 8502, -1, 9534, -1], 'generators': [834823, 835273, 793169, 622537], 'label': '1728.46354.72.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.cx1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336583
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bh1.a1', '24.bw1.a1', '24.bx1.a1', '36.dp1.a1'], 'contains': ['144.r1.a1', '144.x1.a1', '144.bp1.a1', '216.bc1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5719, -1, 5659, -1, 2583, -1, 3742, -1], 'generators': [834823, 1634131, 793169, 1341703], 'label': '1728.46354.72.cy1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '72.cy1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336584
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '24.by1.a1', '36.bl1.a1', '36.dn1.a1', '36.ds1.a1'], 'contains': ['144.s1.a1', '144.v1.a1', '144.bk1.a1', '216.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1557, -1, 8098, -1, 8571, -1, 7721, -1], 'generators': [834823, 1634131, 793169, 622105], 'label': '1728.46354.72.cz1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cz1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336585
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '24.by1.a1', '36.bm1.a1', '36.dq1.a1', '36.du1.a1'], 'contains': ['144.t1.a1', '144.w1.a1', '144.bn1.a1', '216.bc1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1891, -1, 7602, -1, 7426, -1, 9034, -1], 'generators': [834823, 1634131, 793169, 622537], 'label': '1728.46354.72.da1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.da1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336586
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '36.bl1.a1', '36.do1.a1', '36.dt1.a1'], 'contains': ['144.v1.a1', '144.z1.a1', '144.bk1.a1', '216.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [161, -1, 9468, -1, 9717, -1, 8519, -1], 'generators': [834823, 793657, 793169, 622105], 'label': '1728.46354.72.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.db1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336587
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '24.cc1.a1', '24.cd1.a1', '36.bt1.a1', '36.dn1.a1', '36.dt1.a1'], 'contains': ['144.b1.a1', '144.v1.a1', '144.bc1.a1', '216.be1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1218, -1, 7808, -1, 8364, -1, 7526, -1], 'generators': [1675405, 835777, 793169, 622105], 'label': '1728.46354.72.dc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.dc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336588
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '36.bt1.a1', '36.do1.a1', '36.ds1.a1'], 'contains': ['144.v1.a1', '144.bc1.a1', '144.bj1.a1', '216.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [289, -1, 9503, -1, 9692, -1, 8498, -1], 'generators': [1675405, 1674955, 793169, 622105], 'label': '1728.46354.72.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.dd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336589
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '36.bm1.a1', '36.dr1.a1', '36.dv1.a1'], 'contains': ['144.w1.a1', '144.ba1.a1', '144.bn1.a1', '216.bd1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [489, -1, 9030, -1, 8901, -1, 9735, -1], 'generators': [834823, 793657, 793169, 622537], 'label': '1728.46354.72.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.de1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336590
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.h1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.h1.a1', '24.bw1.a1', '24.bx1.a1', '24.by1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6690, -1, 5575, -1, 2905, -1, 3746, -1], 'generators': [834823, 622105, 622537, 1634131, 793169, 1341703], 'label': '1728.46354.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336591
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '24.ce1.a1', '36.bw1.a1', '36.dq1.a1', '36.dv1.a1'], 'contains': ['144.w1.a1', '144.bd1.a1', '144.bl1.a1', '216.be1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1461, -1, 7756, -1, 7359, -1, 9091, -1], 'generators': [1675405, 835777, 793169, 622537], 'label': '1728.46354.72.df1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.df1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336592
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '36.bw1.a1', '36.dr1.a1', '36.du1.a1'], 'contains': ['144.w1.a1', '144.bd1.a1', '144.bm1.a1', '216.bf1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [672, -1, 9091, -1, 8640, -1, 9716, -1], 'generators': [1675405, 1674955, 793169, 622537], 'label': '1728.46354.72.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.dg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336593
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bm1.a1', '24.cc1.a1', '24.ce1.a1', '36.dp1.a1'], 'contains': ['144.x1.a1', '144.bf1.a1', '144.bo1.a1', '216.be1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7107, -1, 4102, -1, 2413, -1, 4706, -1], 'generators': [1675405, 835777, 793169, 1341703], 'label': '1728.46354.72.dh1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '72.dh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336594
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bn1.a1', '24.cd1.a1', '24.ce1.a1'], 'contains': ['144.y1.a1', '144.bh1.a1', '144.br1.a1', '216.be1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8175, -1, 2525, -1, 2254, -1, 5867, -1], 'generators': [1675405, 835777, 793169, 767155], 'label': '1728.46354.72.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1.a1', 'old_label': '72.di1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336595
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '36.d1.a1'], 'contains': ['144.bs1.a1', '144.bu1.a1', '144.cc1.a1', '144.dt1.a1', '144.dt1.b1', '144.dw1.a1', '144.dw1.b1', '216.bg1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3282, -1, 9654, -1, 9945, -1, 9193, -1], 'generators': [46999, 1674451, 1633643, 622105], 'label': '1728.46354.72.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.dj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336596
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '36.j1.a1'], 'contains': ['144.bt1.a1', '144.bv1.a1', '144.cd1.a1', '144.dv1.a1', '144.dv1.b1', '144.dx1.a1', '144.dx1.b1', '216.bg1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3422, -1, 9302, -1, 8799, -1, 9954, -1], 'generators': [46999, 1674451, 1633643, 622537], 'label': '1728.46354.72.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '72.dk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336597
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.r1.a1'], 'contains': ['144.bu1.a1', '144.bz1.a1', '144.ch1.a1', '144.dy1.a1', '144.dy1.b1', '144.eb1.a1', '144.eb1.b1', '216.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2038, -1, 9629, -1, 9269, -1, 8433, -1], 'generators': [46999, 1634131, 1633643, 622105], 'label': '1728.46354.72.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '72.dl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336598
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.s1.a1'], 'contains': ['144.bv1.a1', '144.ca1.a1', '144.ci1.a1', '144.dz1.a1', '144.dz1.b1', '144.ec1.a1', '144.ec1.b1', '216.bh1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2331, -1, 9357, -1, 8229, -1, 9228, -1], 'generators': [46999, 1634131, 1633643, 622537], 'label': '1728.46354.72.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '72.dm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336599
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.t1.a1'], 'contains': ['144.bw1.a1', '144.cb1.a1', '144.cj1.a1', '144.ea1.a1', '144.ea1.b1', '144.ed1.a1', '144.ed1.b1', '216.bh1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4041, -1, 7427, -1, 7284, -1, 7589, -1], 'generators': [46999, 1634131, 1633643, 47089], 'label': '1728.46354.72.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '72.dn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336600
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.t1.a1'], 'contains': ['144.bw1.a1', '144.cb1.a2', '144.cj1.a1', '144.ea1.a2', '144.ea1.b2', '144.ed1.a2', '144.ed1.b2', '216.bh1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4041, -1, 7403, -1, 7284, -1, 7624, -1], 'generators': [46999, 793657, 1633643, 47089], 'label': '1728.46354.72.dn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '72.dn1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336601
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.h1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.g1.a1', '24.ca1.a1', '24.cc1.a1', '24.cd1.a1', '24.ce1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7284, -1, 3949, -1, 2565, -1, 4471, -1], 'generators': [1675405, 622105, 622537, 835777, 793169, 1341703], 'label': '1728.46354.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336602
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '36.be1.a1'], 'contains': ['144.bx1.a1', '144.ch1.a1', '144.ck1.a1', '216.bi1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [800, -1, 9544, -1, 9764, -1, 8632, -1], 'generators': [812125, 1651771, 1633643, 622105], 'label': '1728.46354.72.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.be1.a1', 'old_label': '72.do1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336603
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '36.bj1.a1'], 'contains': ['144.by1.a1', '144.ci1.a1', '144.cl1.a1', '216.bi1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1501, -1, 9153, -1, 8742, -1, 9774, -1], 'generators': [812125, 1651771, 1633643, 622537], 'label': '1728.46354.72.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bj1.a1', 'old_label': '72.dp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336604
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '36.bs1.a1'], 'contains': ['144.cc1.a1', '144.ce1.a1', '144.ck1.a1', '216.bj1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2706, -1, 9565, -1, 9834, -1, 8652, -1], 'generators': [812125, 1656811, 1633643, 622105], 'label': '1728.46354.72.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bs1.a1', 'old_label': '72.dq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336605
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '36.bv1.a1'], 'contains': ['144.cd1.a1', '144.cf1.a1', '144.cl1.a1', '216.bj1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2962, -1, 9167, -1, 8766, -1, 9831, -1], 'generators': [812125, 1656811, 1633643, 622537], 'label': '1728.46354.72.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bv1.a1', 'old_label': '72.dr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336606
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '36.cl1.a1', '36.dw1.a1', '36.dw1.b1'], 'contains': ['144.bs1.a1', '144.bx1.a1', '144.cm1.a1', '144.cp1.a1', '144.cu1.a1', '216.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5214, -1, 5018, -1, 4969, -1, 5531, -1], 'generators': [1674451, 817145, 887131, 622105], 'label': '1728.46354.72.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ds1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336607
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '36.a1.a1', '36.dx1.a1', '36.dx1.b1'], 'contains': ['144.bt1.a1', '144.by1.a1', '144.cn1.a1', '144.cq1.a1', '144.cv1.a1', '216.bk1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5560, -1, 5330, -1, 4927, -1, 5566, -1], 'generators': [1674451, 817145, 887131, 622537], 'label': '1728.46354.72.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.dt1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336608
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.co1.a1', '36.dw1.a1', '36.dy1.a1'], 'contains': ['144.cm1.a1', '144.cr1.a1', '144.dh1.b1', '216.bl1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6239, -1, 4369, -1, 4295, -1, 4474, -1], 'generators': [46999, 817145, 622105, 887131], 'label': '1728.46354.72.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.du1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336609
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.b1', '36.co1.a1', '36.dw1.b1', '36.dy1.b1'], 'contains': ['144.cm1.a1', '144.cr1.b1', '144.dh1.a1', '216.bl1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6239, -1, 4583, -1, 4295, -1, 4504, -1], 'generators': [70957, 817145, 622105, 887131], 'label': '1728.46354.72.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.du1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336610
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.cp1.a1', '36.dx1.a1', '36.dz1.a1'], 'contains': ['144.cn1.a1', '144.cs1.a1', '144.dk1.b1', '216.bl1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6267, -1, 4612, -1, 4066, -1, 4535, -1], 'generators': [46999, 817145, 622537, 887131], 'label': '1728.46354.72.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.dv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336611
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.b1', '36.cp1.a1', '36.dx1.b1', '36.dz1.b1'], 'contains': ['144.cn1.a1', '144.cs1.b1', '144.dk1.a1', '216.bl1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6267, -1, 4741, -1, 4066, -1, 4769, -1], 'generators': [70957, 817145, 622537, 887131], 'label': '1728.46354.72.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.dv1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336612
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.cw1.a1', '24.cx1.a1', '24.cy1.a1', '24.cz1.a1', '32.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9179, -1, 1214, -1, 1059, -1, 1423, -1], 'generators': [1674451, 622537, 70633, 1341703, 622105, 887131], 'label': '1728.46354.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336613
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.cq1.a1', '36.ea1.a1', '36.ea1.a2'], 'contains': ['144.co1.a1', '144.ct1.a1', '144.dn1.b1', '216.bl1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7085, -1, 2581, -1, 3298, -1, 2703, -1], 'generators': [46999, 817145, 47089, 887131], 'label': '1728.46354.72.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.dw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336614
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.b1', '36.cq1.a1', '36.ea1.b1', '36.ea1.b2'], 'contains': ['144.co1.a1', '144.ct1.b1', '144.dn1.a1', '216.bl1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7085, -1, 2906, -1, 3298, -1, 2612, -1], 'generators': [70957, 817145, 47089, 887131], 'label': '1728.46354.72.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.dw1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336615
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.cs1.a1', '36.dy1.a1', '36.dy1.b1'], 'contains': ['144.bz1.a1', '144.ce1.a1', '144.cm1.a1', '144.cw1.a1', '144.db1.a1', '216.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5151, -1, 3978, -1, 4234, -1, 4266, -1], 'generators': [1634131, 817145, 887131, 622105], 'label': '1728.46354.72.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.dx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336616
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.ct1.a1', '36.dz1.a1', '36.dz1.b1'], 'contains': ['144.ca1.a1', '144.cf1.a1', '144.cn1.a1', '144.cx1.a1', '144.dc1.a1', '216.bm1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5182, -1, 4177, -1, 4027, -1, 4371, -1], 'generators': [1634131, 817145, 887131, 622537], 'label': '1728.46354.72.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.dy1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336617
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.cu1.a1', '36.ea1.a1', '36.ea1.b1'], 'contains': ['144.cb1.a1', '144.cg1.a1', '144.co1.a1', '144.cy1.a1', '144.dd1.a1', '216.bm1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6679, -1, 2611, -1, 3453, -1, 2993, -1], 'generators': [1634131, 817145, 887131, 47089], 'label': '1728.46354.72.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.dz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336618
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.cu1.a1', '36.ea1.a2', '36.ea1.b2'], 'contains': ['144.cb1.a2', '144.cg1.a1', '144.co1.a1', '144.cy1.a2', '144.dd1.a2', '216.bm1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6679, -1, 2781, -1, 3453, -1, 3028, -1], 'generators': [1656811, 817145, 887131, 47089], 'label': '1728.46354.72.dz1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.dz1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336619
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '36.cv1.a1', '36.dw1.a1', '36.dw1.b1'], 'contains': ['144.cm1.a1', '144.cz1.a1', '144.di1.a1', '216.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6320, -1, 4878, -1, 4763, -1, 5144, -1], 'generators': [1675405, 817145, 622105, 887131], 'label': '1728.46354.72.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ea1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336620
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '36.cw1.a1', '36.dx1.a1', '36.dx1.b1'], 'contains': ['144.cn1.a1', '144.da1.a1', '144.dl1.a1', '216.bn1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6297, -1, 5226, -1, 4732, -1, 5231, -1], 'generators': [1675405, 817145, 887131, 622537], 'label': '1728.46354.72.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.eb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336621
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.cz1.a1', '36.dy1.a1', '36.dy1.b1'], 'contains': ['144.cm1.a1', '144.de1.a1', '144.dj1.a1', '216.bo1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5745, -1, 3706, -1, 3548, -1, 3843, -1], 'generators': [1633789, 817145, 887131, 622105], 'label': '1728.46354.72.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.ec1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336622
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.da1.a1', '36.dz1.a1', '36.dz1.b1'], 'contains': ['144.cn1.a1', '144.df1.a1', '144.dm1.a1', '216.bo1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5763, -1, 4118, -1, 3487, -1, 4043, -1], 'generators': [1633789, 817145, 887131, 622537], 'label': '1728.46354.72.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.ed1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336623
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.dc1.a1', '24.dd1.a1', '24.de1.a1', '24.de1.a2', '24.df1.a1', '32.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8641, -1, 608, -1, 672, -1, 672, -1], 'generators': [1634131, 622105, 622537, 1341703, 887131, 70633], 'label': '1728.46354.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.k1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
  • id: 264336624
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.db1.a1', '36.ea1.a1', '36.ea1.b2'], 'contains': ['144.co1.a1', '144.dg1.a1', '144.do1.a1', '216.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7062, -1, 2761, -1, 3091, -1, 2586, -1], 'generators': [1633789, 817145, 887131, 47089], 'label': '1728.46354.72.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ee1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336625
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.db1.a1', '36.ea1.a2', '36.ea1.b1'], 'contains': ['144.co1.a1', '144.dg1.a2', '144.do1.a2', '216.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7062, -1, 2746, -1, 3091, -1, 2565, -1], 'generators': [1656487, 817145, 887131, 47089], 'label': '1728.46354.72.ee1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ee1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336626
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.d1.a1', '36.dw1.a1', '36.eb1.a1'], 'contains': ['144.cp1.a1', '144.cr1.a1', '144.cz1.a1', '144.dt1.a1', '144.dw1.a1', '216.bp1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6648, -1, 5157, -1, 5366, -1, 5627, -1], 'generators': [46999, 1674451, 887131, 622105], 'label': '1728.46354.72.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ef1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336627
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.b1', '36.d1.a1', '36.dw1.b1', '36.eb1.b1'], 'contains': ['144.cp1.a1', '144.cr1.b1', '144.cz1.a1', '144.dt1.b1', '144.dw1.b1', '216.bp1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6648, -1, 4903, -1, 5366, -1, 5662, -1], 'generators': [793511, 1674451, 887131, 622105], 'label': '1728.46354.72.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ef1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336628
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.a1', '36.h1.a1', '36.dw1.b1', '36.eb1.a1'], 'contains': ['144.cp1.a1', '144.dh1.a1', '144.di1.a1', '216.bq1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6906, -1, 4778, -1, 4527, -1, 5111, -1], 'generators': [70957, 1674451, 622105, 887131], 'label': '1728.46354.72.eg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.eg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336629
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.b1', '36.h1.a1', '36.dw1.a1', '36.eb1.b1'], 'contains': ['144.cp1.a1', '144.dh1.b1', '144.di1.a1', '216.bq1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6906, -1, 4847, -1, 4527, -1, 4886, -1], 'generators': [817469, 1674451, 622105, 887131], 'label': '1728.46354.72.eg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.eg1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336630
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.j1.a1', '36.dx1.a1', '36.ed1.a1'], 'contains': ['144.cq1.a1', '144.cs1.a1', '144.da1.a1', '144.dv1.a1', '144.dx1.a1', '216.bp1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6739, -1, 5355, -1, 5288, -1, 5727, -1], 'generators': [46999, 1674451, 887131, 622537], 'label': '1728.46354.72.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.eh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336631
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.b1', '36.j1.a1', '36.dx1.b1', '36.ed1.b1'], 'contains': ['144.cq1.a1', '144.cs1.b1', '144.da1.a1', '144.dv1.b1', '144.dx1.b1', '216.bp1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6739, -1, 5200, -1, 5288, -1, 5823, -1], 'generators': [793511, 1674451, 887131, 622537], 'label': '1728.46354.72.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.eh1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336632
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.a1', '36.n1.a1', '36.dx1.b1', '36.ed1.a1'], 'contains': ['144.cq1.a1', '144.dk1.a1', '144.dl1.a1', '216.bq1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6980, -1, 4995, -1, 4462, -1, 5205, -1], 'generators': [70957, 1674451, 887131, 622537], 'label': '1728.46354.72.ei1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.ei1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336633
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.b1', '36.n1.a1', '36.dx1.a1', '36.ed1.b1'], 'contains': ['144.cq1.a1', '144.dk1.b1', '144.dl1.a1', '216.bq1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6980, -1, 5084, -1, 4462, -1, 4941, -1], 'generators': [817469, 1674451, 887131, 622537], 'label': '1728.46354.72.ei1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.ei1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336634
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.dg1.a1', '24.dh1.a1', '24.di1.a1', '24.dj1.a1', '32.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9398, -1, 1324, -1, 1546, -1, 1843, -1], 'generators': [1675405, 70633, 887131, 622105, 1341703, 622537], 'label': '1728.46354.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 264336635
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.a1', '36.p1.a1', '36.dw1.a1', '36.eb1.a1'], 'contains': ['144.cr1.a1', '144.cu1.a1', '144.di1.a1', '216.br1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6876, -1, 4961, -1, 4567, -1, 4853, -1], 'generators': [46999, 1651771, 622105, 887131], 'label': '1728.46354.72.ej1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ej1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336636
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.b1', '36.p1.a1', '36.dw1.b1', '36.eb1.b1'], 'contains': ['144.cr1.b1', '144.cu1.a1', '144.di1.a1', '216.br1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6876, -1, 4824, -1, 4567, -1, 5175, -1], 'generators': [793511, 1651771, 622105, 887131], 'label': '1728.46354.72.ej1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.ej1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336637
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.a1', '36.q1.a1', '36.dx1.a1', '36.ed1.a1'], 'contains': ['144.cs1.a1', '144.cv1.a1', '144.dl1.a1', '216.br1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6957, -1, 5247, -1, 4493, -1, 4915, -1], 'generators': [46999, 1651771, 887131, 622537], 'label': '1728.46354.72.ek1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.ek1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336638
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.b1', '36.q1.a1', '36.dx1.b1', '36.ed1.b1'], 'contains': ['144.cs1.b1', '144.cv1.a1', '144.dl1.a1', '216.br1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6957, -1, 5058, -1, 4493, -1, 5252, -1], 'generators': [793511, 1651771, 887131, 622537], 'label': '1728.46354.72.ek1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.ek1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336639
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '36.r1.a1', '36.dy1.a1', '36.ee1.a1'], 'contains': ['144.cr1.a1', '144.cw1.a1', '144.de1.a1', '144.dy1.a1', '144.eb1.a1', '216.bs1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5836, -1, 3819, -1, 4357, -1, 4301, -1], 'generators': [46999, 1634131, 887131, 622105], 'label': '1728.46354.72.el1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.el1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336640
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.b1', '36.r1.a1', '36.dy1.b1', '36.ee1.b1'], 'contains': ['144.cr1.b1', '144.cw1.a1', '144.de1.a1', '144.dy1.b1', '144.eb1.b1', '216.bs1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5836, -1, 4015, -1, 4357, -1, 4336, -1], 'generators': [793511, 1634131, 887131, 622105], 'label': '1728.46354.72.el1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.el1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336641
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '36.s1.a1', '36.dz1.a1', '36.ef1.a1'], 'contains': ['144.cs1.a1', '144.cx1.a1', '144.df1.a1', '144.dz1.a1', '144.ec1.a1', '216.bs1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5950, -1, 4060, -1, 4148, -1, 4406, -1], 'generators': [46999, 1634131, 887131, 622537], 'label': '1728.46354.72.em1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.em1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336642
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.b1', '36.s1.a1', '36.dz1.b1', '36.ef1.b1'], 'contains': ['144.cs1.b1', '144.cx1.a1', '144.df1.a1', '144.dz1.b1', '144.ec1.b1', '216.bs1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5950, -1, 4152, -1, 4148, -1, 4441, -1], 'generators': [793511, 1634131, 887131, 622537], 'label': '1728.46354.72.em1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.em1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336643
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '36.t1.a1', '36.ea1.a1', '36.eg1.a1'], 'contains': ['144.ct1.a1', '144.cy1.a1', '144.dg1.a1', '144.ea1.a1', '144.ed1.a2', '216.bs1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6601, -1, 2978, -1, 3581, -1, 3505, -1], 'generators': [46999, 1634131, 887131, 47089], 'label': '1728.46354.72.en1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.en1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336644
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '36.t1.a1', '36.ea1.a2', '36.eg1.a2'], 'contains': ['144.ct1.a1', '144.cy1.a2', '144.dg1.a2', '144.ea1.a2', '144.ed1.a1', '216.bs1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6601, -1, 3004, -1, 3581, -1, 3540, -1], 'generators': [46999, 1634131, 887131, 1197949], 'label': '1728.46354.72.en1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.en1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336645
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 8, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.dk1.a1', '24.dl1.a1', '24.dm1.a1', '24.dn1.a1', '24.do1.a1', '24.dp1.a1', '24.dp1.a2', '24.dq1.a1', '24.dq1.a2', '32.f1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9427, -1, 468, -1, 303, -1, 519, -1], 'generators': [1633789, 70633, 887131, 1341703, 622537, 622105], 'label': '1728.46354.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.m1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '432.746'}
  • id: 264336646
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.b1', '36.t1.a1', '36.ea1.b1', '36.eg1.b1'], 'contains': ['144.ct1.b1', '144.cy1.a1', '144.dg1.a2', '144.ea1.b1', '144.ed1.b2', '216.bs1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6601, -1, 3530, -1, 3581, -1, 3279, -1], 'generators': [793511, 1634131, 887131, 47089], 'label': '1728.46354.72.en1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.en1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336647
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.b1', '36.t1.a1', '36.ea1.b2', '36.eg1.b2'], 'contains': ['144.ct1.b1', '144.cy1.a2', '144.dg1.a1', '144.ea1.b2', '144.ed1.b1', '216.bs1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6601, -1, 3582, -1, 3581, -1, 3314, -1], 'generators': [793511, 1634131, 887131, 1197949], 'label': '1728.46354.72.en1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.en1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1.b2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336648
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.u1.a1', '36.dy1.a1', '36.ee1.a1'], 'contains': ['144.cr1.a1', '144.db1.a1', '144.dj1.a1', '216.bt1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5789, -1, 3638, -1, 3760, -1, 3675, -1], 'generators': [46999, 1656811, 887131, 622105], 'label': '1728.46354.72.eo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.eo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336649
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.b1', '36.u1.a1', '36.dy1.b1', '36.ee1.b1'], 'contains': ['144.cr1.b1', '144.db1.a1', '144.dj1.a1', '216.bt1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5789, -1, 3773, -1, 3760, -1, 3655, -1], 'generators': [793511, 1656811, 887131, 622105], 'label': '1728.46354.72.eo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.eo1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336650
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.v1.a1', '36.dz1.a1', '36.ef1.a1'], 'contains': ['144.cs1.a1', '144.dc1.a1', '144.dm1.a1', '216.bt1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5911, -1, 3934, -1, 3651, -1, 3934, -1], 'generators': [46999, 1656811, 887131, 622537], 'label': '1728.46354.72.ep1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.ep1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336651
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.b1', '36.v1.a1', '36.dz1.b1', '36.ef1.b1'], 'contains': ['144.cs1.b1', '144.dc1.a1', '144.dm1.a1', '216.bt1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5911, -1, 4132, -1, 3651, -1, 3914, -1], 'generators': [793511, 1656811, 887131, 622537], 'label': '1728.46354.72.ep1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.ep1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336652
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.w1.a1', '36.ea1.a1', '36.eg1.a2'], 'contains': ['144.ct1.a1', '144.dd1.a1', '144.do1.a1', '216.bt1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6111, -1, 3235, -1, 3353, -1, 2844, -1], 'generators': [46999, 1656811, 887131, 1197949], 'label': '1728.46354.72.eq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.eq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336653
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.w1.a1', '36.ea1.a2', '36.eg1.a1'], 'contains': ['144.ct1.a1', '144.dd1.a2', '144.do1.a2', '216.bt1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6111, -1, 3250, -1, 3353, -1, 2896, -1], 'generators': [46999, 1656811, 887131, 47089], 'label': '1728.46354.72.eq1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.eq1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336654
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.b1', '36.w1.a1', '36.ea1.b1', '36.eg1.b2'], 'contains': ['144.ct1.b1', '144.dd1.a1', '144.do1.a2', '216.bt1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6111, -1, 3479, -1, 3353, -1, 2803, -1], 'generators': [793511, 1656811, 887131, 1197949], 'label': '1728.46354.72.eq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.eq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336655
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.b1', '36.w1.a1', '36.ea1.b2', '36.eg1.b1'], 'contains': ['144.ct1.b1', '144.dd1.a2', '144.do1.a1', '216.bt1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6111, -1, 3556, -1, 3353, -1, 2824, -1], 'generators': [793511, 1656811, 887131, 47089], 'label': '1728.46354.72.eq1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.eq1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1.b2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336656
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3456.ma', 'aut_weyl_index': 2, 'centralizer': '864.a1.a1', 'complements': ['864.e1.a1', '864.e1.b1', '864.d1.a1', '864.f1.a1', '864.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '6.z1.a1', '6.ba1.a1', '6.bb1.a1', '8.h1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6685, 5406, 5574, 5920, 2709, 5452, 3558, 5215], 'generators': [834823, 622537, 622105, 1634131, 1341703, 70633, 887131, 793169], 'label': '1728.46354.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 264336657
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.i1.a1', '18.j1.a1', '18.m1.a1', '18.n1.a1', '18.q1.a1', '18.t1.a1', '18.u1.a1', '18.ba1.a1', '18.bd1.a1', '18.bi1.a1', '18.bk1.a1', '27.a1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3502, -1, 6237, -1, 5611, -1, 6081, -1], 'generators': [46999, 887131, 793169, 1674451, 622105, 835777, 70633], 'label': '1728.46354.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336658
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '36.bc1.a1', '36.dw1.b1', '36.eb1.a1'], 'contains': ['144.cu1.a1', '144.cz1.a1', '144.dh1.a1', '216.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6842, -1, 4802, -1, 4628, -1, 5343, -1], 'generators': [70957, 1651771, 622105, 887131], 'label': '1728.46354.72.er1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.er1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336659
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.b1', '36.bc1.a1', '36.dw1.a1', '36.eb1.b1'], 'contains': ['144.cu1.a1', '144.cz1.a1', '144.dh1.b1', '216.bu1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6842, -1, 4933, -1, 4628, -1, 5002, -1], 'generators': [817469, 1651771, 622105, 887131], 'label': '1728.46354.72.er1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.er1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336660
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '36.bh1.a1', '36.dx1.b1', '36.ed1.a1'], 'contains': ['144.cv1.a1', '144.da1.a1', '144.dk1.a1', '216.bu1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6932, -1, 5044, -1, 4598, -1, 5368, -1], 'generators': [70957, 1651771, 887131, 622537], 'label': '1728.46354.72.es1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.es1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336661
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.b1', '36.bh1.a1', '36.dx1.a1', '36.ed1.b1'], 'contains': ['144.cv1.a1', '144.da1.a1', '144.dk1.b1', '216.bu1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6932, -1, 5268, -1, 4598, -1, 5027, -1], 'generators': [817469, 1651771, 887131, 622537], 'label': '1728.46354.72.es1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.es1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336662
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.bn1.a1', '36.dy1.b1', '36.ee1.a1'], 'contains': ['144.cw1.a1', '144.dh1.a1', '144.dj1.a1', '216.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5888, -1, 3671, -1, 3706, -1, 3572, -1], 'generators': [70957, 1634131, 887131, 622105], 'label': '1728.46354.72.et1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.et1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336663
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.b1', '36.bn1.a1', '36.dy1.a1', '36.ee1.b1'], 'contains': ['144.cw1.a1', '144.dh1.b1', '144.dj1.a1', '216.bv1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5888, -1, 3605, -1, 3706, -1, 3798, -1], 'generators': [817469, 1634131, 887131, 622105], 'label': '1728.46354.72.et1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.et1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336664
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.bp1.a1', '36.dz1.b1', '36.ef1.a1'], 'contains': ['144.cx1.a1', '144.dk1.a1', '144.dm1.a1', '216.bv1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6061, -1, 3953, -1, 3620, -1, 3869, -1], 'generators': [70957, 1634131, 887131, 622537], 'label': '1728.46354.72.eu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.eu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336665
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.b1', '36.bp1.a1', '36.dz1.a1', '36.ef1.b1'], 'contains': ['144.cx1.a1', '144.dk1.b1', '144.dm1.a1', '216.bv1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6061, -1, 3878, -1, 3620, -1, 3960, -1], 'generators': [817469, 1634131, 887131, 622537], 'label': '1728.46354.72.eu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.eu1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336666
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.br1.a1', '36.ea1.b1', '36.eg1.a1'], 'contains': ['144.cy1.a1', '144.dn1.a1', '144.do1.a2', '216.bv1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6135, -1, 3274, -1, 3262, -1, 2642, -1], 'generators': [70957, 1634131, 887131, 47089], 'label': '1728.46354.72.ev1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ev1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336667
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.br1.a1', '36.ea1.b2', '36.eg1.a2'], 'contains': ['144.cy1.a2', '144.dn1.a1', '144.do1.a1', '216.bv1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6135, -1, 3320, -1, 3262, -1, 2672, -1], 'generators': [70957, 1634131, 887131, 1197949], 'label': '1728.46354.72.ev1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ev1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336668
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 36, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.r1.a1', '18.s1.a1', '18.v1.a1', '18.bf1.a1', '18.bg1.a1', '18.bh1.a1', '18.bm1.a1', '27.a1.a1', '36.dp1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5454, -1, 5238, -1, 2430, -1, 3346, -1], 'generators': [46999, 887131, 1341703, 1674451, 70633, 835777, 793169], 'label': '1728.46354.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 264336669
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.b1', '36.br1.a1', '36.ea1.a1', '36.eg1.b1'], 'contains': ['144.cy1.a1', '144.dn1.b1', '144.do1.a1', '216.bv1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6135, -1, 2934, -1, 3262, -1, 2870, -1], 'generators': [817469, 1634131, 887131, 47089], 'label': '1728.46354.72.ev1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ev1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336670
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.b1', '36.br1.a1', '36.ea1.a2', '36.eg1.b2'], 'contains': ['144.cy1.a2', '144.dn1.b1', '144.do1.a2', '216.bv1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6135, -1, 2955, -1, 3262, -1, 2921, -1], 'generators': [817469, 1634131, 887131, 1197949], 'label': '1728.46354.72.ev1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ev1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1.b2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336671
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.by1.a1', '36.dy1.b1', '36.ee1.a1'], 'contains': ['144.db1.a1', '144.de1.a1', '144.dh1.a1', '216.bw1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5993, -1, 3741, -1, 3735, -1, 3597, -1], 'generators': [70957, 1656811, 887131, 622105], 'label': '1728.46354.72.ew1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.ew1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336672
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.b1', '36.by1.a1', '36.dy1.a1', '36.ee1.b1'], 'contains': ['144.db1.a1', '144.de1.a1', '144.dh1.b1', '216.bw1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5993, -1, 3623, -1, 3735, -1, 3823, -1], 'generators': [817469, 1656811, 887131, 622105], 'label': '1728.46354.72.ew1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.ew1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336673
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.bz1.a1', '36.dz1.b1', '36.ef1.a1'], 'contains': ['144.dc1.a1', '144.df1.a1', '144.dk1.a1', '216.bw1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6039, -1, 4039, -1, 3675, -1, 3894, -1], 'generators': [70957, 1656811, 887131, 622537], 'label': '1728.46354.72.ex1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.ex1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336674
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.b1', '36.bz1.a1', '36.dz1.a1', '36.ef1.b1'], 'contains': ['144.dc1.a1', '144.df1.a1', '144.dk1.b1', '216.bw1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6039, -1, 3899, -1, 3675, -1, 4022, -1], 'generators': [817469, 1656811, 887131, 622537], 'label': '1728.46354.72.ex1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.ex1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336675
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.ca1.a1', '36.ea1.b1', '36.eg1.a2'], 'contains': ['144.dd1.a1', '144.dg1.a2', '144.dn1.a1', '216.bw1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6763, -1, 3361, -1, 3328, -1, 2763, -1], 'generators': [70957, 1656811, 887131, 1197949], 'label': '1728.46354.72.ey1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ey1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336676
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '36.ca1.a1', '36.ea1.b2', '36.eg1.a1'], 'contains': ['144.dd1.a2', '144.dg1.a1', '144.dn1.a1', '216.bw1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6763, -1, 3412, -1, 3328, -1, 2783, -1], 'generators': [70957, 1656811, 887131, 47089], 'label': '1728.46354.72.ey1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ey1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336677
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.b1', '36.ca1.a1', '36.ea1.a1', '36.eg1.b2'], 'contains': ['144.dd1.a1', '144.dg1.a1', '144.dn1.b1', '216.bw1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6763, -1, 3163, -1, 3328, -1, 2946, -1], 'generators': [817469, 1656811, 887131, 1197949], 'label': '1728.46354.72.ey1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ey1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336678
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.b1', '36.ca1.a1', '36.ea1.a2', '36.eg1.b1'], 'contains': ['144.dd1.a2', '144.dg1.a2', '144.dn1.b1', '216.bw1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6763, -1, 3178, -1, 3328, -1, 2966, -1], 'generators': [817469, 1656811, 887131, 47089], 'label': '1728.46354.72.ey1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.ey1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1.b2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336679
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1'], 'contains': ['18.e1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1', '18.k1.a1', '18.l1.a1', '18.o1.a1', '18.p1.a1', '18.x1.a1', '18.y1.a1', '18.z1.a1', '18.bb1.a1', '18.be1.a1', '18.bj1.a1', '18.bl1.a1', '27.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3569, -1, 6113, -1, 5414, -1, 6230, -1], 'generators': [46999, 887131, 793169, 1674451, 622537, 835777, 70633], 'label': '1728.46354.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336680
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '24.cx1.a1', '36.cl1.a1', '36.eb1.a1', '36.eb1.b1'], 'contains': ['144.c1.a1', '144.cp1.a1', '144.cu1.a1', '216.bx1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8285, -1, 2353, -1, 3223, -1, 3063, -1], 'generators': [1674451, 887131, 70633, 622105], 'label': '1728.46354.72.ez1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.ez1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336681
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '24.cy1.a1', '36.cm1.a1', '36.ec1.a1', '36.ec1.b1'], 'contains': ['144.e1.a1', '216.bx1.a1', '288.o1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9277, -1, 1562, -1, 1308, -1, 1222, -1], 'generators': [1674451, 1341703, 887131, 70633], 'label': '1728.46354.72.fa1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.fa1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336682
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '24.cz1.a1', '36.cn1.a1'], 'contains': ['144.dq1.a1', '216.bx1.a1', '288.p1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9092, -1, 1540, -1, 326, -1, 462, -1], 'generators': [1674451, 766291, 887131, 70633], 'label': '1728.46354.72.fb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1.a1', 'old_label': '72.fb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 264336683
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '24.cy1.a1', '24.cz1.a1', '36.a1.a1', '36.ed1.a1', '36.ed1.b1'], 'contains': ['144.d1.a1', '144.cq1.a1', '144.cv1.a1', '216.bx1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8323, -1, 2298, -1, 3058, -1, 2736, -1], 'generators': [1674451, 887131, 70633, 622537], 'label': '1728.46354.72.fc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.fc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336684
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.da1.a1', '36.co1.a1', '36.eb1.a1', '36.ee1.a1'], 'contains': ['144.c1.a1', '144.cr1.a1', '144.dh1.a1', '216.by1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8213, -1, 2128, -1, 3018, -1, 2448, -1], 'generators': [46999, 70633, 622105, 887131], 'label': '1728.46354.72.fd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.fd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336685
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.da1.b1', '36.co1.a1', '36.eb1.b1', '36.ee1.b1'], 'contains': ['144.c1.a1', '144.cr1.b1', '144.dh1.b1', '216.by1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8213, -1, 2060, -1, 3018, -1, 2478, -1], 'generators': [793511, 70633, 622105, 887131], 'label': '1728.46354.72.fd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.fd1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336686
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.da1.a1', '36.cp1.a1', '36.ed1.a1', '36.ef1.a1'], 'contains': ['144.d1.a1', '144.cs1.a1', '144.dk1.a1', '216.by1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8248, -1, 2150, -1, 2982, -1, 2509, -1], 'generators': [46999, 70633, 622537, 887131], 'label': '1728.46354.72.fe1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.fe1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336687
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.da1.b1', '36.cp1.a1', '36.ed1.b1', '36.ef1.b1'], 'contains': ['144.d1.a1', '144.cs1.b1', '144.dk1.b1', '216.by1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8248, -1, 2088, -1, 2982, -1, 2540, -1], 'generators': [793511, 70633, 622537, 887131], 'label': '1728.46354.72.fe1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.fe1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336688
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1.a1', '24.db1.a1', '36.cq1.a1', '36.eg1.a1', '36.eg1.a2'], 'contains': ['144.ct1.a1', '144.dn1.a1', '144.dp1.a1', '216.by1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8153, -1, 1774, -1, 2760, -1, 2036, -1], 'generators': [46999, 70633, 47089, 887131], 'label': '1728.46354.72.ff1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.ff1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336689
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1.b1', '24.db1.b1', '36.cq1.a1', '36.eg1.b1', '36.eg1.b2'], 'contains': ['144.ct1.b1', '144.dn1.b1', '144.dp1.a1', '216.by1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8153, -1, 1352, -1, 2760, -1, 2136, -1], 'generators': [793511, 70633, 47089, 887131], 'label': '1728.46354.72.ff1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '72.ff1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336690
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': ['144.ee1.a1', '144.ee1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.o1.a1', '6.q1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '24.i1.a1', '24.cj1.a1', '24.cx1.a1', '36.a1.a1', '36.cl1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5103, 9683, 5405, 515, 4479, 9414, 5024, 2723], 'generators': [1674451, 622537, 622105, 793169, 887131, 70633], 'label': '1728.46354.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336691
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '24.dd1.a1', '24.de1.a1', '24.de1.a2', '36.cr1.a1', '36.eh1.a1', '36.eh1.b1'], 'contains': ['144.e1.a1', '216.bz1.a1', '288.x1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8956, -1, 88, -1, 704, -1, 198, -1], 'generators': [1634131, 1341703, 887131, 70633], 'label': '1728.46354.72.fg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '72.fg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336692
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '24.df1.a1', '36.cs1.a1', '36.ee1.a1', '36.ee1.b1'], 'contains': ['144.c1.a1', '144.cw1.a1', '144.db1.a1', '216.bz1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7864, -1, 1849, -1, 2900, -1, 2301, -1], 'generators': [1634131, 887131, 70633, 622105], 'label': '1728.46354.72.fh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '72.fh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336693
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '72.fi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '24.df1.a1', '36.ct1.a1', '36.ef1.a1', '36.ef1.b1'], 'contains': ['144.d1.a1', '144.cx1.a1', '144.dc1.a1', '216.bz1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7908, -1, 1874, -1, 2836, -1, 2415, -1], 'generators': [1634131, 887131, 70633, 622537], 'label': '1728.46354.72.fi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '72.fi1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fi1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336694
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '24.df1.a1', '36.cu1.a1', '36.eg1.a1', '36.eg1.b1'], 'contains': ['144.cy1.a1', '144.dd1.a2', '144.dp1.a1', '216.bz1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7946, -1, 1635, -1, 2696, -1, 2069, -1], 'generators': [1634131, 887131, 70633, 47089], 'label': '1728.46354.72.fj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '72.fj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336695
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a2', '24.df1.a1', '36.cu1.a1', '36.eg1.a2', '36.eg1.b2'], 'contains': ['144.cy1.a2', '144.dd1.a1', '144.dp1.a1', '216.bz1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7946, -1, 1660, -1, 2696, -1, 2103, -1], 'generators': [1634131, 887131, 70633, 1197949], 'label': '1728.46354.72.fj1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '72.fj1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336696
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.fk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1.a1', '24.dh1.a1', '24.di1.a1', '36.cv1.a1', '36.eb1.a1', '36.eb1.b1'], 'contains': ['144.c1.a1', '144.cz1.a1', '144.di1.a1', '216.ca1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8433, -1, 2248, -1, 3183, -1, 3127, -1], 'generators': [1675405, 70633, 622105, 887131], 'label': '1728.46354.72.fk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '72.fk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336697
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.fl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1.a1', '24.dj1.a1', '36.cw1.a1', '36.ed1.a1', '36.ed1.b1'], 'contains': ['144.d1.a1', '144.da1.a1', '144.dl1.a1', '216.ca1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8379, -1, 2278, -1, 3152, -1, 3251, -1], 'generators': [1675405, 70633, 887131, 622537], 'label': '1728.46354.72.fl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '72.fl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336698
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '72.fm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1.a1', '24.dj1.a1', '36.cx1.a1', '36.ec1.a1', '36.ec1.b1'], 'contains': ['144.e1.a1', '216.ca1.a1', '288.bd1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9355, -1, 1388, -1, 1580, -1, 1263, -1], 'generators': [1675405, 1341703, 887131, 70633], 'label': '1728.46354.72.fm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.fm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336699
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '72.fn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.di1.a1', '24.dj1.a1', '36.cy1.a1'], 'contains': ['144.dr1.a1', '216.ca1.a1', '288.be1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9555, -1, 1087, -1, 1857, -1, 1965, -1], 'generators': [1675405, 767155, 887131, 70633], 'label': '1728.46354.72.fn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bu1.a1', 'old_label': '72.fn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336700
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1.a1', '24.dl1.a1', '24.dm1.a1', '36.cz1.a1', '36.ee1.a1', '36.ee1.b1'], 'contains': ['144.c1.a1', '144.de1.a1', '144.dj1.a1', '216.cb1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7979, -1, 1497, -1, 2729, -1, 2253, -1], 'generators': [1633789, 70633, 887131, 622105], 'label': '1728.46354.72.fo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '72.fo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336701
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': ['144.dy1.a1', '144.eb1.a1', '144.ea1.a2', '144.ed1.a1', '144.ea1.a1', '144.ed1.a2', '144.dy1.b1', '144.eb1.b1', '144.ea1.b2', '144.ed1.b1', '144.ea1.b1', '144.ed1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.p1.a1', '6.r1.a1'], 'contains': ['24.c1.a1', '24.cy1.a1', '36.a1.a1', '36.cm1.a1', '48.i1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6915, 6168, 2810, 3659, 1793, 7450, 2190, 6200], 'generators': [1674451, 622537, 70633, 793169, 1341703, 887131], 'label': '1728.46354.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336702
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1.a1', '24.dn1.a1', '24.do1.a1', '36.da1.a1', '36.ef1.a1', '36.ef1.b1'], 'contains': ['144.d1.a1', '144.df1.a1', '144.dm1.a1', '216.cb1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7997, -1, 1823, -1, 2663, -1, 2273, -1], 'generators': [1633789, 70633, 887131, 622537], 'label': '1728.46354.72.fp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.fp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336703
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1.a1', '24.dp1.a1', '24.dq1.a1', '36.db1.a1', '36.eg1.a1', '36.eg1.b2'], 'contains': ['144.dg1.a1', '144.do1.a2', '144.dp1.a1', '216.cb1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9463, -1, 1328, -1, 2638, -1, 1370, -1], 'generators': [1633789, 70633, 887131, 47089], 'label': '1728.46354.72.fq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.fq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336704
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1.a1', '24.dp1.a2', '24.dq1.a2', '36.db1.a1', '36.eg1.a2', '36.eg1.b1'], 'contains': ['144.dg1.a2', '144.do1.a1', '144.dp1.a1', '216.cb1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9463, -1, 1308, -1, 2638, -1, 1350, -1], 'generators': [1633789, 70633, 887131, 1197949], 'label': '1728.46354.72.fq1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '72.fq1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1.a2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336705
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '72.fr1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1.a1', '24.dn1.a1', '24.dp1.a1', '24.dp1.a2', '36.dc1.a1', '36.eh1.a1', '36.eh1.b1'], 'contains': ['144.e1.a1', '216.cb1.a1', '288.bl1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9174, -1, 52, -1, 354, -1, 144, -1], 'generators': [1633789, 1341703, 887131, 70633], 'label': '1728.46354.72.fr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '72.fr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fr1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336706
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.fs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1.a1', '24.do1.a1', '24.dq1.a1', '24.dq1.a2', '36.dd1.a1'], 'contains': ['144.dq1.a1', '216.cb1.a1', '288.bm1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9668, -1, 282, -1, 52, -1, 111, -1], 'generators': [1633789, 766291, 887131, 70633], 'label': '1728.46354.72.fs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dd1.a1', 'old_label': '72.fs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fs1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336707
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '72.ft1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a1', '24.dn1.a1', '24.dq1.a1', '24.dq1.a2', '36.de1.a1'], 'contains': ['144.dr1.a1', '216.cb1.a1', '288.bn1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9865, -1, 262, -1, 169, -1, 255, -1], 'generators': [1633789, 767155, 887131, 70633], 'label': '1728.46354.72.ft1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.de1.a1', 'old_label': '72.ft1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ft1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336708
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a1', '24.do1.a1', '24.dp1.a1', '24.dq1.a2', '36.df1.a1'], 'contains': ['144.ds1.a1', '216.cb1.a1', '288.bo1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9966, -1, 132, -1, 33, -1, 95, -1], 'generators': [1633789, 1342135, 887131, 70633], 'label': '1728.46354.72.fu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.df1.a1', 'old_label': '72.fu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336709
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a1', '24.do1.a1', '24.dp1.a2', '24.dq1.a1', '36.df1.a1'], 'contains': ['144.ds1.a1', '216.cb1.a1', '288.bo1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9966, -1, 150, -1, 33, -1, 79, -1], 'generators': [1633789, 191707, 887131, 70633], 'label': '1728.46354.72.fu1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.df1.a1', 'old_label': '72.fu1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336710
    {'ambient': '1728.46354', 'aut_centralizer_order': 1728, 'aut_label': '96.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.g1.a1', '48.k1.a1', '48.o1.a1', '48.s1.a1', '48.w1.a1', '48.x1.a1', '48.be1.a1', '48.bf1.a1'], 'contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1', '288.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1143, 7212, 8855, 3024, 7922, 6963, 8376, 3420], 'generators': [793169, 622537, 622105], 'label': '1728.46354.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': -96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336711
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '32.a1.a1', '48.h1.a1', '48.l1.a1', '48.p1.a1', '48.t1.a1', '48.y1.a1', '48.bg1.a1', '48.bh1.a1'], 'contains': ['192.b1.a1', '288.a1.a1', '288.d1.a1', '288.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7684, -1, 3069, -1, 1839, -1, 1863, -1], 'generators': [793169, 1341703, 622105], 'label': '1728.46354.96.b1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336712
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.c1.a1', '6.l1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1', '36.b1.a1', '36.co1.a1', '48.l1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7965, 517, 2732, 9272, 1850, 574, 1492, 8426], 'generators': [46999, 70633, 887131, 793169, 622105, 1341703], 'label': '1728.46354.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.b1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '864.4673', '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': '48.48'}
  • id: 264336713
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '32.a1.a1', '48.u1.a1', '48.z1.a1', '48.bi1.a1'], 'contains': ['192.c1.a1', '288.a1.a1', '288.f1.a1', '288.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8509, -1, 2352, -1, 1530, -1, 2934, -1], 'generators': [793169, 767155, 622105], 'label': '1728.46354.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '96.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336714
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '32.a1.a1', '48.i1.a1', '48.m1.a1', '48.q1.a1', '48.v1.a1', '48.ba1.a1', '48.bj1.a1', '48.bk1.a1'], 'contains': ['192.d1.a1', '288.b1.a1', '288.d1.a1', '288.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7333, -1, 2708, -1, 1803, -1, 1909, -1], 'generators': [793169, 1341703, 622537], 'label': '1728.46354.96.d1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336715
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '32.a1.a1', '48.j1.a1', '48.bb1.a1', '48.bl1.a1'], 'contains': ['192.e1.a1', '288.b1.a1', '288.e1.a1', '288.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7833, -1, 2111, -1, 855, -1, 1197, -1], 'generators': [793169, 766291, 622537], 'label': '1728.46354.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '96.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336716
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '32.a1.a1', '48.n1.a1', '48.r1.a1', '48.bc1.a1'], 'contains': ['192.f1.a1', '288.c1.a1', '288.d1.a1', '288.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8710, -1, 988, -1, 1206, -1, 873, -1], 'generators': [793169, 1341703, 47089], 'label': '1728.46354.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '96.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336717
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '32.a1.a1', '48.bd1.a1'], 'contains': ['192.g1.a1', '288.c1.a1', '288.e1.a1', '288.f1.a1', '288.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8656, -1, 1614, -1, 891, -1, 1076, -1], 'generators': [793169, 766291, 47089], 'label': '1728.46354.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.f1.a1', 'old_label': '96.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336718
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.bm1.a1', '48.bn1.a1', '48.bo1.a1', '48.bp1.a1', '48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bt1.a1', '48.bu1.a1'], 'contains': ['192.a1.a1', '288.h1.a1', '288.i1.a1', '288.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2774, -1, 9262, -1, 8577, -1, 8806, -1], 'generators': [1633643, 622537, 622105], 'label': '1728.46354.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.h1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336719
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.g1.a1', '48.bu1.a1', '48.bv1.a1', '48.bw1.a1', '48.bw1.b1', '48.bx1.a1', '48.by1.a1', '48.bz1.a1', '48.ca1.a1', '48.cb1.a1', '48.cc1.a1', '48.cc1.b1', '48.cd1.a1', '48.ce1.a1'], 'contains': ['192.a1.a1', '288.k1.a1', '288.l1.a1', '288.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6424, -1, 4525, -1, 4266, -1, 4529, -1], 'generators': [887131, 622537, 622105], 'label': '1728.46354.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.i1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336720
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '32.b1.a1', '48.h1.a1', '48.cj1.a1', '48.cj1.b1'], 'contains': ['192.b1.a1', '288.n1.a1', '288.o1.a1', '288.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9716, -1, 1525, -1, 1464, -1, 1498, -1], 'generators': [1674451, 1341703, 622105], 'label': '1728.46354.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '96.j1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336721
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.bm1.a1', '48.bv1.a1', '48.ck1.a1', '48.ck1.b1'], 'contains': ['192.a1.a1', '288.n1.a1', '288.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4769, -1, 8216, -1, 7545, -1, 8262, -1], 'generators': [1674451, 622105, 622537], 'label': '1728.46354.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.k1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336722
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '32.b1.a1', '48.i1.a1', '48.cl1.a1', '48.cl1.b1'], 'contains': ['192.d1.a1', '288.o1.a1', '288.q1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9184, -1, 1288, -1, 1428, -1, 1578, -1], 'generators': [1674451, 1341703, 622537], 'label': '1728.46354.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '96.l1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336770
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.a1', '36.bh1.a1', '54.g1.a1', '54.h1.a1', '54.i1.a1'], 'contains': ['216.d1.a1', '216.f1.a1', '216.j1.a1', '216.bu1.a1', '216.bu1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2379, -1, 7102, -1, 5860, -1, 6303, -1], 'generators': [70957, 1651771, 793169], 'label': '1728.46354.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336723
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 72, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.w1.a1', '6.y1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.f1.b1', '36.b1.a1', '36.cp1.a1', '48.m1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7374, 2615, 2289, 5669, 1495, 2832, 1931, 9033], 'generators': [46999, 70633, 887131, 793169, 622537, 1341703], 'label': '1728.46354.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.f1.a1', '24.f1.b1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '864.4673', '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': '48.48'}
  • id: 264336724
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1.a1', '32.b1.a1', '48.j1.a1'], 'contains': ['192.e1.a1', '288.p1.a1', '288.q1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9111, -1, 1266, -1, 799, -1, 1106, -1], 'generators': [1674451, 766291, 622537], 'label': '1728.46354.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '96.m1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336725
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.k1.a1', '48.bn1.a1', '48.bw1.a1', '48.ck1.a1', '48.cm1.a1', '48.cn1.a1', '48.co1.a1'], 'contains': ['192.a1.a1', '288.r1.a1', '288.s1.a1', '288.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3601, -1, 9925, -1, 8114, -1, 8406, -1], 'generators': [46999, 622537, 622105], 'label': '1728.46354.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.n1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336726
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '48.k1.a1', '48.bn1.a1', '48.bw1.b1', '48.ck1.b1', '48.cm1.b1', '48.cn1.b1', '48.co1.b1'], 'contains': ['192.a1.a1', '288.r1.b1', '288.s1.b1', '288.t1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3601, -1, 9902, -1, 8114, -1, 8548, -1], 'generators': [793511, 622537, 622105], 'label': '1728.46354.96.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.n1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336727
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '32.c1.a1', '48.l1.a1', '48.cj1.a1', '48.cp1.a1'], 'contains': ['192.b1.a1', '288.r1.a1', '288.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9564, -1, 1093, -1, 1362, -1, 1137, -1], 'generators': [46999, 622105, 1341703], 'label': '1728.46354.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.o1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336728
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '32.c1.b1', '48.l1.a1', '48.cj1.b1', '48.cp1.b1'], 'contains': ['192.b1.a1', '288.r1.b1', '288.u1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9564, -1, 926, -1, 1362, -1, 1167, -1], 'generators': [793511, 622105, 1341703], 'label': '1728.46354.96.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.o1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336729
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '32.c1.a1', '48.m1.a1', '48.cl1.a1', '48.cq1.a1'], 'contains': ['192.d1.a1', '288.s1.a1', '288.u1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9085, -1, 1053, -1, 1326, -1, 1236, -1], 'generators': [46999, 622537, 1341703], 'label': '1728.46354.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.p1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336730
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '32.c1.b1', '48.m1.a1', '48.cl1.b1', '48.cq1.b1'], 'contains': ['192.d1.a1', '288.s1.b1', '288.u1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9085, -1, 884, -1, 1326, -1, 1291, -1], 'generators': [793511, 622537, 1341703], 'label': '1728.46354.96.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '96.p1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336731
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1.a1', '32.c1.a1', '48.n1.a1', '48.cr1.a1', '48.cr1.a2'], 'contains': ['192.f1.a1', '288.t1.a1', '288.u1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9666, -1, 571, -1, 1119, -1, 780, -1], 'generators': [46999, 47089, 1341703], 'label': '1728.46354.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '96.q1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336732
    {'ambient': '1728.46354', 'aut_centralizer_order': 36, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1.b1', '32.c1.b1', '48.n1.a1', '48.cr1.b1', '48.cr1.b2'], 'contains': ['192.f1.a1', '288.t1.b1', '288.u1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9666, -1, 498, -1, 1119, -1, 811, -1], 'generators': [793511, 47089, 1341703], 'label': '1728.46354.96.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '96.q1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336733
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.bm1.a1', '48.bo1.a1', '48.bv1.a1', '48.bx1.a1', '48.cm1.a1', '48.cm1.b1'], 'contains': ['192.a1.a1', '288.v1.a1', '288.w1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3552, -1, 8256, -1, 8329, -1, 8852, -1], 'generators': [835273, 622105, 622537], 'label': '1728.46354.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '96.r1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336734
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.759', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': ['144.du1.a1', '144.du1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.t1.a1', '6.bb1.a1'], 'contains': ['24.a1.a1', '24.j1.a1', '24.l1.a1', '24.cl1.a1', '24.df1.a1', '36.cs1.a1', '36.ct1.a1', '36.cu1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5160, 8553, 5477, 2700, 4017, 8405, 4314, 1783], 'generators': [1634131, 622105, 622537, 793169, 887131, 70633], 'label': '1728.46354.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 264336735
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '32.d1.a1', '48.p1.a1', '48.cp1.a1', '48.cp1.b1'], 'contains': ['192.b1.a1', '288.x1.a1', '288.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8990, -1, 763, -1, 1279, -1, 960, -1], 'generators': [1634131, 1341703, 622105], 'label': '1728.46354.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1.a1', 'old_label': '96.s1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336736
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '32.d1.a1', '48.q1.a1', '48.cq1.a1', '48.cq1.b1'], 'contains': ['192.d1.a1', '288.x1.a1', '288.z1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8928, -1, 641, -1, 1243, -1, 1027, -1], 'generators': [1634131, 1341703, 622537], 'label': '1728.46354.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1.a1', 'old_label': '96.t1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336737
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '32.d1.a1', '48.r1.a1', '48.cr1.a1', '48.cr1.b1'], 'contains': ['192.f1.a1', '288.x1.a1', '288.ba1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9350, -1, 477, -1, 1042, -1, 659, -1], 'generators': [1634131, 1341703, 47089], 'label': '1728.46354.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '96.u1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336738
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a2', '32.d1.a1', '48.r1.a1', '48.cr1.a2', '48.cr1.b2'], 'contains': ['192.f1.a1', '288.x1.a1', '288.ba1.a2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9350, -1, 455, -1, 1042, -1, 689, -1], 'generators': [1634131, 1341703, 1197949], 'label': '1728.46354.96.u1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '96.u1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336739
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.b1.a1', '48.bp1.a1', '48.by1.a1', '48.cn1.a1', '48.cn1.b1'], 'contains': ['192.a1.a1', '288.y1.a1', '288.z1.a1', '288.ba1.a1', '288.ba1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4090, -1, 9341, -1, 6938, -1, 7673, -1], 'generators': [1634131, 622537, 622105], 'label': '1728.46354.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '96.v1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336740
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.s1.a1', '48.bq1.a1', '48.bz1.a1', '48.ck1.a1', '48.ck1.b1', '48.cm1.a1', '48.cm1.b1'], 'contains': ['192.a1.a1', '288.bb1.a1', '288.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3795, -1, 9946, -1, 8613, -1, 8883, -1], 'generators': [1675405, 622105, 622537], 'label': '1728.46354.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.w1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336741
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1.a1', '32.e1.a1', '48.t1.a1', '48.cj1.a1', '48.cj1.b1'], 'contains': ['192.b1.a1', '288.bb1.a1', '288.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9743, -1, 1461, -1, 1698, -1, 1655, -1], 'generators': [1675405, 622105, 1341703], 'label': '1728.46354.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '96.x1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336742
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.di1.a1', '32.e1.a1', '48.u1.a1'], 'contains': ['192.c1.a1', '288.bb1.a1', '288.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9792, -1, 1230, -1, 1886, -1, 1979, -1], 'generators': [1675405, 622105, 767155], 'label': '1728.46354.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1.a1', 'old_label': '96.y1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336743
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1.a1', '32.e1.a1', '48.v1.a1', '48.cl1.a1', '48.cl1.b1'], 'contains': ['192.d1.a1', '288.bc1.a1', '288.bd1.a1', '288.be1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9305, -1, 1248, -1, 1668, -1, 1680, -1], 'generators': [1675405, 1341703, 622537], 'label': '1728.46354.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '96.z1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336744
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '48.bp1.a1', '48.br1.a1', '48.by1.a1', '48.ca1.a1', '48.co1.a1', '48.co1.b1'], 'contains': ['192.a1.a1', '288.bf1.a1', '288.bg1.a1', '288.bh1.a1', '288.bh1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3530, -1, 9207, -1, 7698, -1, 7953, -1], 'generators': [793657, 622537, 622105], 'label': '1728.46354.96.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '96.ba1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336745
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.a1.a1', 'complements': ['144.dy1.a1', '144.eb1.a1', '144.ea1.a2', '144.ed1.a1', '144.ea1.a1', '144.ed1.a2', '144.dy1.b1', '144.eb1.b1', '144.ea1.b2', '144.ed1.b1', '144.ea1.b1', '144.ed1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.ba1.a1', '6.bf1.a1'], 'contains': ['24.c1.a1', '24.dj1.a1', '36.cw1.a1', '36.cx1.a1', '36.cy1.a1', '48.v1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7183, 5151, 2768, 4569, 2118, 5375, 4214, 7045], 'generators': [1675405, 70633, 887131, 793169, 1341703, 622537], 'label': '1728.46354.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336746
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.x1.a1', '48.bs1.a1', '48.cb1.a1', '48.cn1.a1', '48.cn1.b1', '48.co1.a1', '48.co1.b1'], 'contains': ['192.a1.a1', '288.bi1.a1', '288.bj1.a1', '288.bk1.a1', '288.bk1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3205, -1, 9726, -1, 7400, -1, 8005, -1], 'generators': [1633789, 622537, 622105], 'label': '1728.46354.96.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '96.bb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336747
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1.a1', '32.f1.a1', '48.y1.a1', '48.cp1.a1', '48.cp1.b1'], 'contains': ['192.b1.a1', '288.bi1.a1', '288.bl1.a1', '288.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9141, -1, 720, -1, 975, -1, 935, -1], 'generators': [1633789, 1341703, 622105], 'label': '1728.46354.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1.a1', 'old_label': '96.bc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336748
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1.a1', '32.f1.a1', '48.z1.a1'], 'contains': ['192.c1.a1', '288.bi1.a1', '288.bn1.a1', '288.bo1.a1', '288.bo1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9525, -1, 355, -1, 769, -1, 915, -1], 'generators': [1633789, 767155, 622105], 'label': '1728.46354.96.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.z1.a1', 'old_label': '96.bd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336749
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1.a1', '32.f1.a1', '48.ba1.a1', '48.cq1.a1', '48.cq1.b1'], 'contains': ['192.d1.a1', '288.bj1.a1', '288.bl1.a1', '288.bn1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8967, -1, 522, -1, 951, -1, 1002, -1], 'generators': [1633789, 1341703, 622537], 'label': '1728.46354.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1.a1', 'old_label': '96.be1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336750
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1.a1', '32.f1.a1', '48.bb1.a1'], 'contains': ['192.e1.a1', '288.bj1.a1', '288.bm1.a1', '288.bo1.a1', '288.bo1.a2'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9489, -1, 247, -1, 615, -1, 714, -1], 'generators': [1633789, 766291, 622537], 'label': '1728.46354.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bb1.a1', 'old_label': '96.bf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336751
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.a1', '32.f1.a1', '48.bc1.a1', '48.cr1.a1', '48.cr1.b2'], 'contains': ['192.f1.a1', '288.bk1.a1', '288.bl1.a1', '288.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9456, -1, 340, -1, 744, -1, 634, -1], 'generators': [1633789, 1341703, 47089], 'label': '1728.46354.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '96.bg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336752
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1.a2', '32.f1.a1', '48.bc1.a1', '48.cr1.a2', '48.cr1.b1'], 'contains': ['192.f1.a1', '288.bk1.a2', '288.bl1.a1', '288.bo1.a2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9456, -1, 388, -1, 744, -1, 613, -1], 'generators': [1633789, 1341703, 1197949], 'label': '1728.46354.96.bg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bp1.a1', 'old_label': '96.bg1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336753
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '18.4', 'aut_weyl_index': 384, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1.a1', '32.f1.a1', '48.bd1.a1'], 'contains': ['192.g1.a1', '288.bk1.a1', '288.bm1.a1', '288.bn1.a1', '288.bo1.a2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9507, -1, 278, -1, 649, -1, 755, -1], 'generators': [1633789, 766291, 47089], 'label': '1728.46354.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1.a1', 'old_label': '96.bh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336754
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '18.4', 'aut_weyl_index': 384, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1.a2', '32.f1.a1', '48.bd1.a1'], 'contains': ['192.g1.a1', '288.bk1.a2', '288.bm1.a1', '288.bn1.a1', '288.bo1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9507, -1, 263, -1, 649, -1, 735, -1], 'generators': [1633789, 190843, 1197949], 'label': '1728.46354.96.bh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bd1.a1', 'old_label': '96.bh1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 264336755
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.j1.a1', '54.a1.a1', '54.b1.a1', '54.i1.a1'], 'contains': ['216.b1.a1', '216.c1.a1', '216.f1.a1', '216.p1.a1', '216.t1.a1', '216.bg1.a1', '216.bp1.a1', '216.bp1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3437, -1, 7950, -1, 7125, -1, 7236, -1], 'generators': [46999, 1674451, 793169, 887131], 'label': '1728.46354.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336756
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '12.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '72.b1.a1', 'complements': ['144.du1.a1', '144.du1.b1', '144.ee1.a1', '144.ee1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.u1.a1', '6.bc1.a1'], 'contains': ['24.a1.a1', '24.n1.a1', '24.p1.a1', '36.c1.a1', '36.dh1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4490, 7390, 5817, 1658, 5653, 6360, 6315, 816], 'generators': [835777, 622105, 793169, 887131, 70633, 622537], 'label': '1728.46354.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.f1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.c1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336757
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.k1.a1', '54.a1.a1', '54.c1.a1', '54.j1.a1'], 'contains': ['216.b1.a1', '216.e1.a1', '216.i1.a1', '216.q1.a1', '216.r1.a1', '216.y1.a1', '216.z1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3852, -1, 7486, -1, 7096, -1, 7394, -1], 'generators': [1674451, 835777, 887131], 'label': '1728.46354.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336758
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.l1.a1', '54.b1.a1', '54.d1.a1', '54.j1.a1'], 'contains': ['216.b1.a1', '216.g1.a1', '216.k1.a1', '216.r1.a1', '216.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3324, -1, 7655, -1, 6290, -1, 6825, -1], 'generators': [1674451, 811801, 887131], 'label': '1728.46354.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336759
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.m1.a1', '54.a1.a1', '54.d1.a1', '54.k1.a1'], 'contains': ['216.b1.a1', '216.h1.a1', '216.l1.a1', '216.s1.a1', '216.bb1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1469, -1, 7537, -1, 6902, -1, 7211, -1], 'generators': [834823, 1674451, 887131], 'label': '1728.46354.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336760
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '54.c1.a1', '54.d1.a1', '54.i1.a1'], 'contains': ['216.b1.a1', '216.j1.a1', '216.m1.a1', '216.bq1.a1', '216.bq1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4281, -1, 6421, -1, 5572, -1, 6166, -1], 'generators': [70957, 1674451, 793169], 'label': '1728.46354.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336761
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.o1.a1', '54.b1.a1', '54.c1.a1', '54.k1.a1'], 'contains': ['216.b1.a1', '216.n1.a1', '216.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4186, -1, 7966, -1, 6001, -1, 6566, -1], 'generators': [812125, 1674451], 'label': '1728.46354.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336762
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.q1.a1', '54.e1.a1', '54.f1.a1', '54.i1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.m1.a1', '216.br1.a1', '216.br1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2027, -1, 6061, -1, 5738, -1, 6272, -1], 'generators': [46999, 1651771, 793169], 'label': '1728.46354.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336763
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.s1.a1', '36.t1.a1', '54.a1.a1', '54.e1.a1', '54.l1.a1'], 'contains': ['216.c1.a1', '216.e1.a1', '216.h1.a1', '216.u1.a1', '216.v1.a1', '216.bh1.a1', '216.bs1.a1', '216.bs1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2484, -1, 7989, -1, 6659, -1, 6613, -1], 'generators': [46999, 1634131, 793169, 887131], 'label': '1728.46354.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336764
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.v1.a1', '36.w1.a1', '54.b1.a1', '54.f1.a1', '54.l1.a1'], 'contains': ['216.c1.a1', '216.g1.a1', '216.o1.a1', '216.bt1.a1', '216.bt1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3707, -1, 6039, -1, 5612, -1, 6096, -1], 'generators': [46999, 1656811, 793169], 'label': '1728.46354.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336765
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '36.z1.a1', '54.a1.a1', '54.f1.a1', '54.m1.a1'], 'contains': ['216.c1.a1', '216.i1.a1', '216.l1.a1', '216.w1.a1', '216.x1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [814, -1, 6384, -1, 6983, -1, 7293, -1], 'generators': [46999, 835777, 887131], 'label': '1728.46354.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336766
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1.a1', '36.ba1.a1', '54.b1.a1', '54.e1.a1', '54.m1.a1'], 'contains': ['216.c1.a1', '216.k1.a1', '216.n1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2873, -1, 8200, -1, 6220, -1, 6665, -1], 'generators': [46999, 811801], 'label': '1728.46354.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336767
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3456.ma', 'aut_weyl_index': 2, 'centralizer': '864.a1.a1', 'complements': ['864.d1.a1', '864.f1.a1', '864.e1.a1', '864.e1.b1', '864.g1.a1', '864.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.bc1.a1', '6.bd1.a1', '6.be1.a1', '6.bf1.a1', '8.i1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6896, 4470, 3939, 4390, 2445, 4618, 3766, 2710], 'generators': [1675405, 622537, 622105, 835777, 1341703, 70633, 887131, 793169], 'label': '1728.46354.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 264336768
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.b1.a1', 'complements': ['144.dv1.a1', '144.dx1.a1', '144.dv1.b1', '144.dx1.b1', '144.dz1.a1', '144.ec1.a1', '144.ea1.a2', '144.ed1.a1', '144.ea1.a1', '144.ed1.a2', '144.dz1.b1', '144.ec1.b1', '144.ea1.b2', '144.ed1.b1', '144.ea1.b1', '144.ed1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.c1.a1', '6.m1.a1', '6.bd1.a1'], 'contains': ['24.b1.a1', '36.c1.a1', '36.dj1.a1', '48.bg1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4646, 3432, 4215, 6400, 2678, 3561, 3377, 3618], 'generators': [835777, 622105, 70633, 1341703, 793169, 887131], 'label': '1728.46354.12.h1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.h1.a1', 'normal_contained_in': ['4.f1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336769
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1.a1', '36.bg1.a1', '54.e1.a1', '54.g1.a1', '54.j1.a1'], 'contains': ['216.d1.a1', '216.e1.a1', '216.k1.a1', '216.y1.a1', '216.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2535, -1, 8006, -1, 6253, -1, 6693, -1], 'generators': [1651771, 811801, 887131], 'label': '1728.46354.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336771
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1.a1', '36.bi1.a1', '54.f1.a1', '54.h1.a1', '54.j1.a1'], 'contains': ['216.d1.a1', '216.g1.a1', '216.i1.a1', '216.z1.a1', '216.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1298, -1, 6329, -1, 6107, -1, 6794, -1], 'generators': [1651771, 835777, 887131], 'label': '1728.46354.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336772
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1.a1', '36.bj1.a1', '54.e1.a1', '54.h1.a1', '54.k1.a1'], 'contains': ['216.d1.a1', '216.h1.a1', '216.n1.a1', '216.bi1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2165, -1, 8168, -1, 6186, -1, 6637, -1], 'generators': [812125, 1651771, 887131], 'label': '1728.46354.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336773
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1.a1', '36.bk1.a1', '54.f1.a1', '54.g1.a1', '54.k1.a1'], 'contains': ['216.d1.a1', '216.l1.a1', '216.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1414, -1, 6164, -1, 5827, -1, 6409, -1], 'generators': [834823, 1651771], 'label': '1728.46354.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336774
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1.a1', '36.bm1.a1', '54.a1.a1', '54.g1.a1', '54.n1.a1'], 'contains': ['216.e1.a1', '216.f1.a1', '216.l1.a1', '216.bc1.a1', '216.bd1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1592, -1, 7452, -1, 7059, -1, 7260, -1], 'generators': [834823, 1634131, 887131], 'label': '1728.46354.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336775
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1.a1', '36.bp1.a1', '36.br1.a1', '54.c1.a1', '54.g1.a1', '54.l1.a1'], 'contains': ['216.e1.a1', '216.j1.a1', '216.o1.a1', '216.bv1.a1', '216.bv1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4585, -1, 6568, -1, 5450, -1, 5963, -1], 'generators': [70957, 1634131, 793169], 'label': '1728.46354.108.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336776
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bo1.a1', '36.bq1.a1', '54.c1.a1', '54.e1.a1', '54.n1.a1'], 'contains': ['216.e1.a1', '216.m1.a1', '216.n1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4381, -1, 7713, -1, 5949, -1, 6459, -1], 'generators': [812125, 1634131], 'label': '1728.46354.108.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336777
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '36.bv1.a1', '54.b1.a1', '54.h1.a1', '54.n1.a1'], 'contains': ['216.f1.a1', '216.g1.a1', '216.n1.a1', '216.bj1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3290, -1, 7915, -1, 6414, -1, 7000, -1], 'generators': [812125, 1656811, 887131], 'label': '1728.46354.108.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336778
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bt1.a1', '36.bw1.a1', '54.a1.a1', '54.h1.a1', '54.o1.a1'], 'contains': ['216.f1.a1', '216.h1.a1', '216.i1.a1', '216.be1.a1', '216.bf1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1504, -1, 7509, -1, 7023, -1, 7363, -1], 'generators': [1675405, 835777, 887131], 'label': '1728.46354.108.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336779
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 24, 'centralizer': '288.b1.a1', 'complements': ['144.dv1.a1', '144.dx1.a1', '144.dv1.b1', '144.dx1.b1', '144.dz1.a1', '144.ec1.a1', '144.ea1.a2', '144.ed1.a1', '144.ea1.a1', '144.ed1.a2', '144.dz1.b1', '144.ec1.b1', '144.ea1.b2', '144.ed1.b1', '144.ea1.b1', '144.ed1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1', '6.n1.a1', '6.z1.a1'], 'contains': ['24.b1.a1', '36.dg1.a1', '36.dk1.a1', '36.dl1.a1', '48.bh1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6740, 1772, 5612, 8149, 2863, 2080, 2373, 5332], 'generators': [834823, 70633, 887131, 793169, 1341703, 622105], 'label': '1728.46354.12.i1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.i1.a1', 'normal_contained_in': ['4.g1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 264336780
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bu1.a1', '36.bx1.a1', '54.b1.a1', '54.g1.a1', '54.o1.a1'], 'contains': ['216.f1.a1', '216.k1.a1', '216.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3403, -1, 7840, -1, 6032, -1, 6591, -1], 'generators': [1675405, 811801], 'label': '1728.46354.108.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336781
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.by1.a1', '36.bz1.a1', '36.ca1.a1', '54.d1.a1', '54.h1.a1', '54.l1.a1'], 'contains': ['216.g1.a1', '216.h1.a1', '216.j1.a1', '216.bw1.a1', '216.bw1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2130, -1, 7038, -1, 5489, -1, 6066, -1], 'generators': [70957, 1656811, 793169], 'label': '1728.46354.108.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336782
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cb1.a1', '36.cc1.a1', '54.d1.a1', '54.f1.a1', '54.n1.a1'], 'contains': ['216.g1.a1', '216.l1.a1', '216.m1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1353, -1, 6142, -1, 5797, -1, 6434, -1], 'generators': [834823, 1656811], 'label': '1728.46354.108.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336783
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cd1.a1', '36.ce1.a1', '54.d1.a1', '54.e1.a1', '54.o1.a1'], 'contains': ['216.h1.a1', '216.k1.a1', '216.m1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2098, -1, 7286, -1, 5919, -1, 6540, -1], 'generators': [1651447, 811801], 'label': '1728.46354.108.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 264336784
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1.a1', '36.ci1.a1', '54.c1.a1', '54.h1.a1', '54.m1.a1'], 'contains': ['216.i1.a1', '216.j1.a1', '216.n1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1983, -1, 6989, -1, 5975, -1, 6481, -1], 'generators': [70957, 835777], 'label': '1728.46354.108.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336785
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1.a1', '36.cj1.a1', '54.c1.a1', '54.f1.a1', '54.o1.a1'], 'contains': ['216.i1.a1', '216.m1.a1', '216.o1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4316, -1, 5995, -1, 5769, -1, 6349, -1], 'generators': [1651447, 835777], 'label': '1728.46354.108.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336786
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ch1.a1', '36.ck1.a1', '54.d1.a1', '54.g1.a1', '54.m1.a1'], 'contains': ['216.j1.a1', '216.k1.a1', '216.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1781, -1, 6795, -1, 5891, -1, 6329, -1], 'generators': [70957, 811801], 'label': '1728.46354.108.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336787
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.cl1.a1', '36.cm1.a1', '36.cn1.a1', '54.i1.a1', '54.j1.a1', '54.k1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.d1.a1', '216.bk1.a1', '216.bx1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5360, -1, 5477, -1, 4325, -1, 5046, -1], 'generators': [1674451, 793169, 887131, 70633], 'label': '1728.46354.108.bc1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336788
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.co1.a1', '36.cp1.a1', '36.cq1.a1', '54.i1.a1', '54.l1.a1', '54.m1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.j1.a1', '216.bl1.a1', '216.bl1.b1', '216.by1.a1', '216.by1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6119, -1, 4230, -1, 3944, -1, 4105, -1], 'generators': [46999, 793169, 70633], 'label': '1728.46354.108.bd1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336789
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1.a1', '36.cs1.a1', '36.ct1.a1', '36.cu1.a1', '54.j1.a1', '54.l1.a1', '54.n1.a1'], 'contains': ['216.a1.a1', '216.e1.a1', '216.g1.a1', '216.bm1.a1', '216.bz1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5181, -1, 5524, -1, 3783, -1, 4167, -1], 'generators': [1634131, 793169, 887131, 70633], 'label': '1728.46354.108.be1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336790
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.k1.a1', '24.bb1.a1', '24.bi1.a1', '24.cf1.a1', '24.co1.a1', '24.co1.b1', '36.d1.a1', '36.j1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3387, -1, 8090, -1, 8292, -1, 8179, -1], 'generators': [46999, 622537, 622105, 1674451, 793169, 887131], 'label': '1728.46354.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336791
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1.a1', '36.cw1.a1', '36.cx1.a1', '36.cy1.a1', '54.i1.a1', '54.n1.a1', '54.o1.a1'], 'contains': ['216.a1.a1', '216.f1.a1', '216.m1.a1', '216.bn1.a1', '216.ca1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6147, -1, 5501, -1, 4799, -1, 5930, -1], 'generators': [1675405, 793169, 70633], 'label': '1728.46354.108.bf1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336792
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1.a1', '36.da1.a1', '36.db1.a1', '36.dc1.a1', '36.dd1.a1', '36.de1.a1', '36.df1.a1', '54.k1.a1', '54.l1.a1', '54.o1.a1'], 'contains': ['216.a1.a1', '216.h1.a1', '216.o1.a1', '216.bo1.a1', '216.cb1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7055, -1, 2837, -1, 3122, -1, 3158, -1], 'generators': [1633789, 793169, 70633], 'label': '1728.46354.108.bg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336793
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.dh1.a1', '36.dj1.a1', '36.dm1.a1', '54.j1.a1', '54.m1.a1', '54.o1.a1'], 'contains': ['216.a1.a1', '216.i1.a1', '216.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4687, -1, 5945, -1, 5084, -1, 6033, -1], 'generators': [835777, 887131, 70633], 'label': '1728.46354.108.bh1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336794
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dg1.a1', '36.di1.a1', '36.dk1.a1', '36.dl1.a1', '54.k1.a1', '54.m1.a1', '54.n1.a1'], 'contains': ['216.a1.a1', '216.l1.a1', '216.n1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4913, -1, 5967, -1, 5047, -1, 5597, -1], 'generators': [834823, 70633], 'label': '1728.46354.108.bi1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 264336795
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dn1.a1', '36.dp1.a1', '36.dq1.a1', '54.a1.a1'], 'contains': ['216.p1.a1', '216.q1.a1', '216.s1.a1', '216.u1.a1', '216.w1.a1', '216.bc1.a1', '216.be1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4532, -1, 6947, -1, 7245, -1, 7480, -1], 'generators': [46999, 1674451, 835777], 'label': '1728.46354.108.bj1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336796
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.do1.a1', '36.dr1.a1', '54.a1.a1'], 'contains': ['216.p1.a1', '216.r1.a1', '216.s1.a1', '216.v1.a1', '216.x1.a1', '216.bd1.a1', '216.bf1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [451, -1, 9184, -1, 8976, -1, 8801, -1], 'generators': [46999, 1674451, 1674955], 'label': '1728.46354.108.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336797
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ds1.a1', '36.du1.a1', '54.a1.a1'], 'contains': ['216.t1.a1', '216.u1.a1', '216.x1.a1', '216.y1.a1', '216.bb1.a1', '216.bc1.a1', '216.bf1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [408, -1, 9418, -1, 8712, -1, 8735, -1], 'generators': [46999, 835273, 1674955], 'label': '1728.46354.108.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336798
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dt1.a1', '36.dv1.a1', '54.a1.a1'], 'contains': ['216.t1.a1', '216.v1.a1', '216.w1.a1', '216.z1.a1', '216.bb1.a1', '216.bd1.a1', '216.be1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [254, -1, 9095, -1, 9013, -1, 8869, -1], 'generators': [46999, 835273, 835777], 'label': '1728.46354.108.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336799
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dw1.a1', '36.dx1.a1', '54.i1.a1'], 'contains': ['216.bk1.a1', '216.bl1.a1', '216.bn1.a1', '216.bp1.a1', '216.bq1.b1', '216.br1.a1', '216.bu1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6861, -1, 5174, -1, 4665, -1, 4971, -1], 'generators': [46999, 1674451, 817145], 'label': '1728.46354.108.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '108.bn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336800
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dw1.b1', '36.dx1.b1', '54.i1.a1'], 'contains': ['216.bk1.a1', '216.bl1.b1', '216.bn1.a1', '216.bp1.b1', '216.bq1.a1', '216.br1.b1', '216.bu1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6861, -1, 5140, -1, 4665, -1, 5277, -1], 'generators': [70957, 1674451, 817145], 'label': '1728.46354.108.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '108.bn1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336801
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.d1.a1', '24.g1.a1', '24.j1.a1', '24.n1.a1', '24.be1.a1', '24.bs1.a1', '24.bt1.a1', '36.e1.a1', '36.k1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3575, -1, 7697, -1, 8236, -1, 8414, -1], 'generators': [1674451, 622105, 622537, 835777, 887131, 793169], 'label': '1728.46354.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 264336864
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.l1.a1', '72.dl1.a1', '72.dx1.a1'], 'contains': ['288.h1.a1', '288.y1.a1', '288.bf1.a1', '432.p1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3870, -1, 9609, -1, 7633, -1, 7494, -1], 'generators': [1634131, 1633643, 622105], 'label': '1728.46354.144.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '144.bz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336802
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dy1.a1', '36.dz1.a1', '36.ea1.a1', '36.ea1.a2', '54.l1.a1'], 'contains': ['216.bl1.a1', '216.bm1.a1', '216.bo1.a1', '216.bs1.a1', '216.bt1.a1', '216.bv1.b1', '216.bw1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5661, -1, 3399, -1, 3517, -1, 3472, -1], 'generators': [46999, 1634131, 817145], 'label': '1728.46354.108.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '108.bo1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336803
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dy1.b1', '36.dz1.b1', '36.ea1.b1', '36.ea1.b2', '54.l1.a1'], 'contains': ['216.bl1.b1', '216.bm1.a1', '216.bo1.a1', '216.bs1.b1', '216.bt1.b1', '216.bv1.a1', '216.bw1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5661, -1, 3537, -1, 3517, -1, 3441, -1], 'generators': [70957, 1634131, 817145], 'label': '1728.46354.108.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '108.bo1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336804
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eb1.a1', '36.ec1.a1', '36.ed1.a1', '54.i1.a1'], 'contains': ['216.bp1.a1', '216.bq1.a1', '216.br1.a1', '216.bu1.a1', '216.bx1.a1', '216.by1.a1', '216.ca1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8323, -1, 2278, -1, 3414, -1, 3096, -1], 'generators': [46999, 1674451, 70633], 'label': '1728.46354.108.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '108.bp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336805
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eb1.b1', '36.ec1.b1', '36.ed1.b1', '54.i1.a1'], 'contains': ['216.bp1.b1', '216.bq1.b1', '216.br1.b1', '216.bu1.b1', '216.bx1.a1', '216.by1.b1', '216.ca1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8323, -1, 2331, -1, 3414, -1, 3226, -1], 'generators': [793511, 1674451, 70633], 'label': '1728.46354.108.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '108.bp1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336806
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ee1.a1', '36.ef1.a1', '36.eg1.a1', '36.eg1.a2', '36.eh1.a1', '54.l1.a1'], 'contains': ['216.bs1.a1', '216.bt1.a1', '216.bv1.a1', '216.bw1.a1', '216.by1.a1', '216.bz1.a1', '216.cb1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7891, -1, 1955, -1, 2797, -1, 2196, -1], 'generators': [46999, 1634131, 70633], 'label': '1728.46354.108.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '108.bq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336807
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ee1.b1', '36.ef1.b1', '36.eg1.b1', '36.eg1.b2', '36.eh1.b1', '54.l1.a1'], 'contains': ['216.bs1.b1', '216.bt1.b1', '216.bv1.b1', '216.bw1.b1', '216.by1.b1', '216.bz1.a1', '216.cb1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7891, -1, 1657, -1, 2797, -1, 2227, -1], 'generators': [793511, 1634131, 70633], 'label': '1728.46354.108.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1.a1', 'old_label': '108.bq1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336808
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.c1.a1', 'complements': ['12.ct1.a1', '12.cv1.a2', '12.cv1.a1', '12.ct1.b1', '12.cv1.b2', '12.cv1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.i1.a1', '48.j1.a1', '72.f1.a1', '72.by1.a1', '72.bz1.a1', '72.ca1.a1', '72.cb1.a1'], 'contains': ['288.b1.a1', '288.q1.a1', '432.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4247, 7904, 7603, 2603, 7002, 7580, 7837, 3888], 'generators': [1674451, 793169, 622537], 'label': '1728.46354.144.a1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.a1.a1', '48.a1.a1'], 'normal_contains': ['288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.42', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336809
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.d1.a1', 'complements': ['12.cr1.a1', '12.cr1.b1', '12.cu1.a1', '12.cv1.a2', '12.cv1.a1', '12.cu1.b1', '12.cv1.b2', '12.cv1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.bg1.a1', '48.bi1.a1', '72.w1.a1', '72.bt1.a1', '72.ck1.a1', '72.cr1.a1', '72.dc1.a1'], 'contains': ['288.a1.a1', '432.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [970, 6211, 7059, 3944, 7376, 6412, 7240, 2908], 'generators': [835777, 793169, 622105], 'label': '1728.46354.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.c1.a1', '48.c1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.42', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336810
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.a1.a1', 'complements': ['12.ck1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.e1.a1', '48.cf1.a1', '72.a1.a1', '72.ez1.a1', '72.fd1.a1', '72.fd1.b1', '72.fh1.a1', '72.fk1.a1', '72.fo1.a1'], 'contains': ['288.k1.a1', '432.a1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8144, 3745, 2005, 6444, 2905, 4256, 2453, 5309], 'generators': [887131, 70633, 622105], 'label': '1728.46354.144.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.c1.a1', 'normal_contained_in': ['48.d1.a1', '48.e1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '12.4', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336811
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '12.g1.a1', 'complements': ['12.ch1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.f1.a1', '48.cg1.a1', '72.b1.a1', '72.fc1.a1', '72.fe1.a1', '72.fe1.b1', '72.fi1.a1', '72.fl1.a1', '72.fp1.a1'], 'contains': ['288.l1.a1', '432.a1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8200, 5184, 2042, 5601, 2868, 5491, 2505, 5921], 'generators': [887131, 70633, 622537], 'label': '1728.46354.144.d1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.d1.a1', 'normal_contained_in': ['48.d1.a1', '48.f1.a1', '72.b1.a1'], 'normal_contains': ['432.a1.a1', '576.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '12.4', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336812
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.g1.a1', '24.l1.a1', '24.p1.a1', '24.be1.a1', '24.bu1.a1', '36.f1.a1', '36.l1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3110, -1, 7626, -1, 7817, -1, 7825, -1], 'generators': [1674451, 622105, 622537, 811801, 887131, 793169], 'label': '1728.46354.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336813
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.e1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '24.d1.a1', 'complements': ['12.ci1.a1', '12.cm1.a1', '12.cj1.a1', '12.cl1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.f1.a1', '48.ch1.a1', '72.c1.a1', '72.d1.a1', '72.d1.b1', '72.fa1.a1', '72.fg1.a1', '72.fm1.a1', '72.fr1.a1'], 'contains': ['432.a1.a1', '576.d1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9244, 2610, 805, 7310, 1146, 3426, 553, 6874], 'generators': [1341703, 887131, 70633], 'label': '1728.46354.144.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '144.e1.a1', 'normal_contained_in': ['48.e1.a1', '48.f1.a1', '72.c1.a1', '72.d1.a1', '72.d1.b1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336814
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.a1.a1', '72.e1.a1', '72.g1.a1', '72.j1.a1', '72.l1.a1', '72.o1.a1', '72.q1.a1', '72.t1.a1', '72.w1.a1', '72.x1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1'], 'contains': ['288.a1.a1', '288.h1.a1', '288.k1.a1', '432.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2397, -1, 7210, -1, 7326, -1, 6950, -1], 'generators': [793169, 887131, 622105], 'label': '1728.46354.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336815
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '6.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.b1.a1', '72.f1.a1', '72.h1.a1', '72.k1.a1', '72.m1.a1', '72.p1.a1', '72.r1.a1', '72.u1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1', '72.bi1.a1', '72.bj1.a1'], 'contains': ['288.b1.a1', '288.i1.a1', '288.l1.a1', '432.b1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2684, -1, 7189, -1, 6628, -1, 7647, -1], 'generators': [793169, 887131, 622537], 'label': '1728.46354.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336816
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.i1.a1', '72.n1.a1', '72.s1.a1', '72.v1.a1', '72.bk1.a1', '72.bl1.a1', '72.bm1.a1'], 'contains': ['288.c1.a1', '288.j1.a1', '288.m1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5169, -1, 5039, -1, 5162, -1, 5396, -1], 'generators': [793169, 887131, 47089], 'label': '1728.46354.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336817
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.h1.a1', '72.e1.a1', '72.bq1.a1', '72.bt1.a1', '72.bu1.a1', '72.bv1.a1'], 'contains': ['288.a1.a1', '288.n1.a1', '432.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3913, -1, 7701, -1, 7805, -1, 7281, -1], 'generators': [1674451, 793169, 622105], 'label': '1728.46354.144.i1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336818
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cm1.a1', '48.h1.a1', '48.i1.a1', '72.br1.a1', '72.bs1.a1', '72.bw1.a1'], 'contains': ['288.d1.a1', '288.o1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7314, -1, 2948, -1, 1941, -1, 1940, -1], 'generators': [1674451, 793169, 1341703], 'label': '1728.46354.144.j1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '144.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336819
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1.a1', '48.h1.a1', '48.j1.a1', '72.bx1.a1'], 'contains': ['288.e1.a1', '288.p1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7779, -1, 2214, -1, 1006, -1, 1322, -1], 'generators': [1674451, 793169, 766291], 'label': '1728.46354.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ba1.a1', 'old_label': '144.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336820
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.l1.a1', '72.g1.a1', '72.bq1.a1', '72.cc1.a1', '72.ce1.a1', '72.ch1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1', '288.r1.a1', '288.r1.b1', '432.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [915, -1, 8804, -1, 8443, -1, 7781, -1], 'generators': [46999, 793169, 622105], 'label': '1728.46354.144.l1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336821
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.m1.a1', '72.h1.a1', '72.by1.a1', '72.cd1.a1', '72.cf1.a1', '72.ci1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.b1.a1', '288.s1.a1', '288.s1.b1', '432.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [993, -1, 8461, -1, 7450, -1, 8657, -1], 'generators': [46999, 793169, 622537], 'label': '1728.46354.144.m1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336822
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.n1.a1', '72.i1.a1', '72.cg1.a1', '72.cj1.a1'], 'contains': ['288.c1.a1', '288.t1.a1', '288.t1.b1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4997, -1, 5908, -1, 5792, -1, 6593, -1], 'generators': [46999, 793169, 47089], 'label': '1728.46354.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '144.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336823
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '6.q1.a1'], 'contains': ['24.g1.a1', '24.m1.a1', '24.q1.a1', '24.bf1.a1', '24.bv1.a1', '36.g1.a1', '36.m1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1790, -1, 7521, -1, 8020, -1, 8132, -1], 'generators': [834823, 622105, 622537, 1674451, 887131, 793169], 'label': '1728.46354.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336824
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '72.br1.a1', '72.co1.a1', '72.cp1.a1'], 'contains': ['288.d1.a1', '288.u1.a1', '288.u1.b1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7618, -1, 2082, -1, 1775, -1, 1528, -1], 'generators': [46999, 793169, 1341703], 'label': '1728.46354.144.o1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '144.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336825
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.e1.a1', '72.j1.a1', '72.cc1.a1', '72.cq1.a1', '72.cr1.a1', '72.cs1.a1', '72.ct1.a1'], 'contains': ['288.a1.a1', '288.v1.a1', '432.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [888, -1, 8857, -1, 8669, -1, 7890, -1], 'generators': [835273, 793169, 622105], 'label': '1728.46354.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336826
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.f1.a1', '72.k1.a1', '72.cd1.a1', '72.cu1.a1', '72.cv1.a1', '72.cw1.a1', '72.cx1.a1'], 'contains': ['288.b1.a1', '288.w1.a1', '432.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1229, -1, 9063, -1, 7778, -1, 8747, -1], 'generators': [835273, 793169, 622537], 'label': '1728.46354.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336827
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '144.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1.a1', '48.p1.a1', '48.q1.a1', '48.r1.a1', '72.bs1.a1', '72.co1.a1', '72.cy1.a1'], 'contains': ['288.d1.a1', '288.x1.a1', '432.f1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7449, -1, 2769, -1, 1747, -1, 1624, -1], 'generators': [1634131, 793169, 1341703], 'label': '1728.46354.144.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '144.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336828
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.p1.a1', '72.l1.a1', '72.bt1.a1', '72.ce1.a1', '72.cq1.a1', '72.cz1.a1'], 'contains': ['288.a1.a1', '288.y1.a1', '432.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3588, -1, 8428, -1, 7614, -1, 7189, -1], 'generators': [1634131, 793169, 622105], 'label': '1728.46354.144.s1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336829
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.q1.a1', '72.m1.a1', '72.bz1.a1', '72.cf1.a1', '72.cu1.a1', '72.da1.a1'], 'contains': ['288.b1.a1', '288.z1.a1', '432.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3682, -1, 7717, -1, 6982, -1, 7971, -1], 'generators': [1634131, 793169, 622537], 'label': '1728.46354.144.t1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '144.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336830
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.r1.a1', '72.n1.a1', '72.cg1.a1'], 'contains': ['288.c1.a1', '288.ba1.a1', '288.ba1.a2', '432.f1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5140, -1, 5529, -1, 5653, -1, 6199, -1], 'generators': [1634131, 793169, 47089], 'label': '1728.46354.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '144.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336831
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.t1.a1', '48.u1.a1', '72.o1.a1', '72.bq1.a1', '72.cc1.a1', '72.cz1.a1', '72.db1.a1', '72.dc1.a1', '72.dd1.a1'], 'contains': ['288.a1.a1', '288.bb1.a1', '432.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1418, -1, 8555, -1, 8540, -1, 7556, -1], 'generators': [1675405, 793169, 622105], 'label': '1728.46354.144.v1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336832
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.v1.a1', '72.p1.a1', '72.by1.a1', '72.cd1.a1', '72.da1.a1', '72.de1.a1', '72.df1.a1', '72.dg1.a1'], 'contains': ['288.b1.a1', '288.bc1.a1', '432.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1569, -1, 8347, -1, 7517, -1, 8829, -1], 'generators': [1675405, 793169, 622537], 'label': '1728.46354.144.w1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336833
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cx1.a1', '48.t1.a1', '48.v1.a1', '72.br1.a1', '72.cy1.a1', '72.dh1.a1'], 'contains': ['288.d1.a1', '288.bd1.a1', '432.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7392, -1, 2979, -1, 2328, -1, 3812, -1], 'generators': [1675405, 793169, 1341703], 'label': '1728.46354.144.x1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ch1.a1', 'old_label': '144.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336834
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.o1.a1', '24.r1.a1', '24.cp1.a1', '24.cp1.b1', '36.h1.a1', '36.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4130, -1, 6836, -1, 6234, -1, 6368, -1], 'generators': [70957, 622537, 887131, 1674451, 793169, 622105], 'label': '1728.46354.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336835
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cy1.a1', '48.u1.a1', '48.v1.a1', '72.di1.a1'], 'contains': ['288.f1.a1', '288.be1.a1', '432.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8079, -1, 2357, -1, 2132, -1, 5790, -1], 'generators': [1675405, 793169, 767155], 'label': '1728.46354.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cd1.a1', 'old_label': '144.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336836
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '72.l1.a1', '72.q1.a1', '72.bu1.a1', '72.ch1.a1', '72.cr1.a1', '72.cs1.a1', '72.db1.a1'], 'contains': ['288.a1.a1', '288.bf1.a1', '432.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1530, -1, 8654, -1, 8415, -1, 7934, -1], 'generators': [793657, 793169, 622105], 'label': '1728.46354.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336837
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '72.m1.a1', '72.r1.a1', '72.ca1.a1', '72.ci1.a1', '72.cv1.a1', '72.cw1.a1', '72.de1.a1'], 'contains': ['288.b1.a1', '288.bg1.a1', '432.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1840, -1, 8826, -1, 7720, -1, 8618, -1], 'generators': [793657, 793169, 622537], 'label': '1728.46354.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '144.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336838
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '72.n1.a1', '72.s1.a1', '72.cj1.a1'], 'contains': ['288.c1.a1', '288.bh1.a1', '288.bh1.a2', '432.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3885, -1, 6813, -1, 5764, -1, 6666, -1], 'generators': [793657, 793169, 47089], 'label': '1728.46354.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.bb1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336839
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '48.y1.a1', '48.z1.a1', '72.t1.a1', '72.bv1.a1', '72.ce1.a1', '72.ch1.a1', '72.ct1.a1', '72.dc1.a1', '72.dd1.a1'], 'contains': ['288.a1.a1', '288.bi1.a1', '432.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [837, -1, 8538, -1, 7853, -1, 7367, -1], 'generators': [1633789, 793169, 622105], 'label': '1728.46354.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bc1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336840
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '48.ba1.a1', '48.bb1.a1', '72.u1.a1', '72.cb1.a1', '72.cf1.a1', '72.ci1.a1', '72.cx1.a1', '72.df1.a1', '72.dg1.a1'], 'contains': ['288.b1.a1', '288.bj1.a1', '432.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1599, -1, 8054, -1, 7102, -1, 8219, -1], 'generators': [1633789, 793169, 622537], 'label': '1728.46354.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.bd1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336841
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '48.bc1.a1', '48.bd1.a1', '72.v1.a1', '72.cg1.a1', '72.cj1.a1'], 'contains': ['288.c1.a1', '288.bk1.a1', '288.bk1.a2', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5017, -1, 5419, -1, 5614, -1, 6216, -1], 'generators': [1633789, 793169, 47089], 'label': '1728.46354.144.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.be1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336842
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1.a1', '48.y1.a1', '48.ba1.a1', '48.bc1.a1', '72.bw1.a1', '72.co1.a1', '72.dh1.a1'], 'contains': ['288.d1.a1', '288.bl1.a1', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7487, -1, 2453, -1, 1502, -1, 1472, -1], 'generators': [1633789, 793169, 1341703], 'label': '1728.46354.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.dp1.a1', 'old_label': '144.bf1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336843
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1.a1', '48.y1.a1', '48.bb1.a1', '48.bd1.a1', '72.bx1.a1'], 'contains': ['288.e1.a1', '288.bm1.a1', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7740, -1, 2107, -1, 827, -1, 984, -1], 'generators': [1633789, 793169, 766291], 'label': '1728.46354.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bx1.a1', 'old_label': '144.bg1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336844
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1.a1', '48.z1.a1', '48.ba1.a1', '48.bd1.a1', '72.di1.a1'], 'contains': ['288.f1.a1', '288.bn1.a1', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8450, -1, 2405, -1, 1400, -1, 1886, -1], 'generators': [1633789, 793169, 767155], 'label': '1728.46354.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.di1.a1', 'old_label': '144.bh1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336845
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.q1.a1'], 'contains': ['24.g1.a1', '24.s1.a1', '24.t1.a1', '36.i1.a1', '36.o1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3860, -1, 7668, -1, 7030, -1, 7182, -1], 'generators': [812125, 622105, 622537, 1674451, 1633643, 887131], 'label': '1728.46354.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336846
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.df1.a1', '48.z1.a1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1'], 'contains': ['288.g1.a1', '288.bo1.a1', '288.bo1.a2', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [8704, -1, 1411, -1, 722, -1, 896, -1], 'generators': [1633789, 793169, 1342135], 'label': '1728.46354.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bi1.a1', 'old_label': '144.bi1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336847
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1.a1', '72.w1.a1', '72.y1.a1', '72.bu1.a1', '72.cl1.a1', '72.cq1.a1', '72.cs1.a1', '72.dd1.a1'], 'contains': ['288.a1.a1', '432.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1125, -1, 8641, -1, 8510, -1, 7916, -1], 'generators': [1674955, 793169, 622105], 'label': '1728.46354.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.bj1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336848
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1.a1', '48.bh1.a1', '72.z1.a1', '72.bv1.a1', '72.ck1.a1', '72.cl1.a1', '72.ct1.a1', '72.cz1.a1', '72.db1.a1'], 'contains': ['288.a1.a1', '432.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [363, -1, 7748, -1, 7972, -1, 7512, -1], 'generators': [834823, 793169, 622105], 'label': '1728.46354.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.bk1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336849
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '6.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.bj1.a1', '72.bd1.a1', '72.bz1.a1', '72.cm1.a1', '72.cv1.a1', '72.df1.a1'], 'contains': ['288.b1.a1', '432.j1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1244, -1, 7097, -1, 7062, -1, 8025, -1], 'generators': [835777, 622537, 793169], 'label': '1728.46354.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '144.bl1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336850
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1.a1', '72.bd1.a1', '72.bf1.a1', '72.ca1.a1', '72.cn1.a1', '72.cu1.a1', '72.cw1.a1', '72.dg1.a1'], 'contains': ['288.b1.a1', '432.k1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1824, -1, 8839, -1, 7654, -1, 8765, -1], 'generators': [1674955, 622537, 793169], 'label': '1728.46354.144.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '144.bm1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336851
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1.a1', '48.bk1.a1', '48.bl1.a1', '72.bg1.a1', '72.cb1.a1', '72.cm1.a1', '72.cn1.a1', '72.cx1.a1', '72.da1.a1', '72.de1.a1'], 'contains': ['288.b1.a1', '432.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [952, -1, 7627, -1, 7255, -1, 8237, -1], 'generators': [834823, 622537, 793169], 'label': '1728.46354.144.bn1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.bn1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336852
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '48.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dj1.a1', '48.bg1.a1', '48.bj1.a1', '72.bs1.a1', '72.cp1.a1', '72.dh1.a1'], 'contains': ['288.d1.a1', '432.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4892, -1, 4130, -1, 2421, -1, 3759, -1], 'generators': [835777, 1341703, 793169], 'label': '1728.46354.144.bo1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '144.bo1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336853
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '144.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dk1.a1', '48.bh1.a1', '48.bk1.a1', '72.bw1.a1', '72.cp1.a1', '72.cy1.a1'], 'contains': ['288.d1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5524, -1, 5980, -1, 2535, -1, 3180, -1], 'generators': [834823, 793169, 1341703], 'label': '1728.46354.144.bp1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ck1.a1', 'old_label': '144.bp1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336854
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.a1', '48.bh1.a1', '48.bl1.a1', '72.bx1.a1'], 'contains': ['288.e1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7471, -1, 3325, -1, 2026, -1, 1389, -1], 'generators': [834823, 793169, 766291], 'label': '1728.46354.144.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1.a1', 'old_label': '144.bq1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336855
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '48.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1.a1', '48.bi1.a1', '48.bj1.a1', '72.di1.a1'], 'contains': ['288.f1.a1', '432.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7283, -1, 2688, -1, 2271, -1, 5860, -1], 'generators': [835777, 767155, 793169], 'label': '1728.46354.144.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ce1.a1', 'old_label': '144.br1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336856
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.h1.a1', '24.i1.a1', '24.r1.a1', '24.cq1.a1', '24.cq1.b1', '36.p1.a1', '36.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2607, -1, 6540, -1, 6460, -1, 6547, -1], 'generators': [46999, 622537, 887131, 1651771, 793169, 622105], 'label': '1728.46354.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336857
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '72.e1.a1', '72.dj1.a1', '72.ds1.a1'], 'contains': ['288.h1.a1', '288.n1.a1', '288.v1.a1', '432.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3818, -1, 8031, -1, 8479, -1, 8196, -1], 'generators': [1674451, 1633643, 622105], 'label': '1728.46354.144.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '144.bs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336858
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '72.f1.a1', '72.dk1.a1', '72.dt1.a1'], 'contains': ['288.i1.a1', '288.q1.a1', '288.w1.a1', '432.m1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3941, -1, 7729, -1, 7497, -1, 8731, -1], 'generators': [1674451, 1633643, 622537], 'label': '1728.46354.144.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.bt1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336859
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '72.g1.a1', '72.dj1.a1', '72.dl1.a1'], 'contains': ['288.h1.a1', '288.r1.a1', '288.r1.b1', '432.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2314, -1, 9850, -1, 8705, -1, 8309, -1], 'generators': [46999, 1633643, 622105], 'label': '1728.46354.144.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.bu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336860
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '72.h1.a1', '72.dk1.a1', '72.dm1.a1'], 'contains': ['288.i1.a1', '288.s1.a1', '288.s1.b1', '432.n1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2355, -1, 9592, -1, 8077, -1, 8913, -1], 'generators': [46999, 1633643, 622537], 'label': '1728.46354.144.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.bv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336861
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '72.i1.a1', '72.dn1.a1', '72.dn1.a2'], 'contains': ['288.j1.a1', '288.t1.a1', '288.t1.b1', '432.n1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4160, -1, 7286, -1, 7205, -1, 7471, -1], 'generators': [46999, 1633643, 47089], 'label': '1728.46354.144.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '144.bw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336862
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '72.j1.a1', '72.do1.a1', '72.ds1.a1'], 'contains': ['288.h1.a1', '288.v1.a1', '432.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1065, -1, 6752, -1, 8387, -1, 7860, -1], 'generators': [1651771, 1633643, 622105], 'label': '1728.46354.144.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '144.bx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336863
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '72.k1.a1', '72.dp1.a1', '72.dt1.a1'], 'contains': ['288.i1.a1', '288.w1.a1', '432.o1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1755, -1, 6736, -1, 7478, -1, 8715, -1], 'generators': [1651771, 1633643, 622537], 'label': '1728.46354.144.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '144.by1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336865
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.m1.a1', '72.dm1.a1', '72.dy1.a1'], 'contains': ['288.i1.a1', '288.z1.a1', '288.bg1.a1', '432.p1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4116, -1, 9275, -1, 7083, -1, 7804, -1], 'generators': [1634131, 1633643, 622537], 'label': '1728.46354.144.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.ca1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336866
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.n1.a1', '72.dn1.a1', '72.dz1.a1'], 'contains': ['288.j1.a1', '288.ba1.a1', '288.bh1.a1', '432.p1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4188, -1, 6924, -1, 6834, -1, 6737, -1], 'generators': [1634131, 1633643, 47089], 'label': '1728.46354.144.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.cb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336867
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.t1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.m1.a1', '24.bj1.a1', '24.bk1.a1', '24.cg1.a1', '24.cr1.a1', '24.cr1.b1', '36.r1.a1', '36.s1.a1', '36.t1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2729, -1, 7969, -1, 7621, -1, 7604, -1], 'generators': [46999, 622105, 622537, 1634131, 793169, 887131], 'label': '1728.46354.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336868
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '72.n1.a1', '72.dn1.a2', '72.dz1.a2'], 'contains': ['288.j1.a1', '288.ba1.a2', '288.bh1.a2', '432.p1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4188, -1, 6844, -1, 6834, -1, 6753, -1], 'generators': [793657, 1633643, 47089], 'label': '1728.46354.144.cb1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.cb1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336869
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '72.o1.a1', '72.dj1.a1', '72.dq1.a1'], 'contains': ['288.h1.a1', '288.bb1.a1', '432.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2772, -1, 9670, -1, 8803, -1, 8578, -1], 'generators': [1675405, 1633643, 622105], 'label': '1728.46354.144.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '144.cc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336870
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '72.p1.a1', '72.dk1.a1', '72.dr1.a1'], 'contains': ['288.i1.a1', '288.bc1.a1', '432.q1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3164, -1, 9244, -1, 8301, -1, 8988, -1], 'generators': [1675405, 1633643, 622537], 'label': '1728.46354.144.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.cd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336871
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '72.q1.a1', '72.dq1.a1', '72.dx1.a1'], 'contains': ['288.h1.a1', '288.bf1.a1', '432.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2860, -1, 6895, -1, 7894, -1, 7691, -1], 'generators': [1656811, 1633643, 622105], 'label': '1728.46354.144.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bi1.a1', 'old_label': '144.ce1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336872
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '72.r1.a1', '72.dr1.a1', '72.dy1.a1'], 'contains': ['288.i1.a1', '288.bg1.a1', '432.r1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3232, -1, 6775, -1, 7422, -1, 8285, -1], 'generators': [1656811, 1633643, 622537], 'label': '1728.46354.144.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1.a1', 'old_label': '144.cf1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336873
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '72.s1.a1', '72.dz1.a1', '72.dz1.a2'], 'contains': ['288.j1.a1', '288.bh1.a1', '288.bh1.a2', '432.r1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4976, -1, 2871, -1, 5672, -1, 5419, -1], 'generators': [1656811, 1633643, 47089], 'label': '1728.46354.144.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '144.cg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336874
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.t1.a1', '72.dl1.a1', '72.do1.a1'], 'contains': ['288.h1.a1', '288.bi1.a1', '432.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1086, -1, 9639, -1, 8641, -1, 8091, -1], 'generators': [1633789, 1633643, 622105], 'label': '1728.46354.144.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.ch1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336875
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.u1.a1', '72.dm1.a1', '72.dp1.a1'], 'contains': ['288.i1.a1', '288.bj1.a1', '432.s1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1884, -1, 9233, -1, 7833, -1, 8783, -1], 'generators': [1633789, 1633643, 622537], 'label': '1728.46354.144.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1.a1', 'old_label': '144.ci1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336876
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.v1.a1', '72.dn1.a1', '72.dn1.a2'], 'contains': ['288.j1.a1', '288.bk1.a1', '288.bk1.a2', '432.s1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4138, -1, 7269, -1, 7177, -1, 7447, -1], 'generators': [1633789, 1633643, 47089], 'label': '1728.46354.144.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.cj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336877
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.bb1.a1', '72.do1.a1', '72.dq1.a1'], 'contains': ['288.h1.a1', '432.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2458, -1, 9652, -1, 8736, -1, 8350, -1], 'generators': [812125, 1633643, 622105], 'label': '1728.46354.144.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.ck1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336878
    {'ambient': '1728.46354', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 6, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1', '6.v1.a1', '6.z1.a1', '6.bd1.a1', '9.a1.a1', '9.b1.a1', '12.ch1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6627, -1, 5259, -1, 2505, -1, 3379, -1], 'generators': [46999, 1341703, 622105, 1674451, 793169, 70633, 887131, 835777], 'label': '1728.46354.3.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': '864.4673', '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': '288.1028'}
  • id: 264336879
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '6.t1.a1'], 'contains': ['24.h1.a1', '24.l1.a1', '24.t1.a1', '24.cs1.a1', '24.cs1.b1', '36.u1.a1', '36.v1.a1', '36.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3476, -1, 6290, -1, 6292, -1, 5865, -1], 'generators': [46999, 622105, 622537, 1656811, 793169, 887131], 'label': '1728.46354.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336880
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.bi1.a1', '72.dp1.a1', '72.dr1.a1'], 'contains': ['288.i1.a1', '432.t1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2647, -1, 9220, -1, 8182, -1, 8938, -1], 'generators': [812125, 622537, 1633643], 'label': '1728.46354.144.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1.a1', 'old_label': '144.cl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336881
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '72.a1.a1', '72.ds1.a1', '72.du1.a1', '72.du1.b1', '72.dx1.a1', '72.ea1.a1', '72.ec1.a1'], 'contains': ['288.h1.a1', '288.k1.a1', '432.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5458, -1, 4664, -1, 4339, -1, 4590, -1], 'generators': [817145, 887131, 622105], 'label': '1728.46354.144.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336882
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '144.cn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '72.b1.a1', '72.dt1.a1', '72.dv1.a1', '72.dv1.b1', '72.dy1.a1', '72.eb1.a1', '72.ed1.a1'], 'contains': ['288.i1.a1', '288.l1.a1', '432.u1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5501, -1, 4746, -1, 4210, -1, 4681, -1], 'generators': [817145, 887131, 622537], 'label': '1728.46354.144.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336883
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '72.bm1.a1', '72.dw1.a1', '72.dw1.b1', '72.dz1.a1', '72.dz1.a2', '72.ee1.a1', '72.ee1.a2'], 'contains': ['288.j1.a1', '288.m1.a1', '432.u1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7230, -1, 2706, -1, 3471, -1, 2758, -1], 'generators': [817145, 887131, 47089], 'label': '1728.46354.144.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.co1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.co1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336884
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.cp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '72.e1.a1', '72.ds1.a1', '72.ef1.a1', '72.ef1.b1', '72.eg1.a1', '72.eg1.b1', '72.ez1.a1'], 'contains': ['288.k1.a1', '288.n1.a1', '288.v1.a1', '432.v1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6538, -1, 4892, -1, 5322, -1, 5573, -1], 'generators': [1674451, 887131, 622105], 'label': '1728.46354.144.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '144.cp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336885
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '144.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '72.f1.a1', '72.dt1.a1', '72.eh1.a1', '72.eh1.b1', '72.ei1.a1', '72.ei1.b1', '72.fc1.a1'], 'contains': ['288.l1.a1', '288.q1.a1', '288.w1.a1', '432.v1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6691, -1, 5281, -1, 5190, -1, 5645, -1], 'generators': [1674451, 887131, 622537], 'label': '1728.46354.144.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.cq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336886
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '72.g1.a1', '72.du1.a1', '72.ef1.a1', '72.ej1.a1', '72.el1.a1', '72.eo1.a1', '72.fd1.a1'], 'contains': ['288.k1.a1', '288.r1.a1', '432.w1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6326, -1, 4368, -1, 4375, -1, 4559, -1], 'generators': [46999, 887131, 622105], 'label': '1728.46354.144.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336887
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.b1', '72.g1.a1', '72.du1.b1', '72.ef1.b1', '72.ej1.b1', '72.el1.b1', '72.eo1.b1', '72.fd1.b1'], 'contains': ['288.k1.a1', '288.r1.b1', '432.w1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6326, -1, 4622, -1, 4375, -1, 4620, -1], 'generators': [793511, 887131, 622105], 'label': '1728.46354.144.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cr1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336888
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '72.h1.a1', '72.dv1.a1', '72.eh1.a1', '72.ek1.a1', '72.em1.a1', '72.ep1.a1', '72.fe1.a1'], 'contains': ['288.l1.a1', '288.s1.a1', '432.w1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6360, -1, 4515, -1, 4302, -1, 4651, -1], 'generators': [46999, 887131, 622537], 'label': '1728.46354.144.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cs1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336889
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.b1', '72.h1.a1', '72.dv1.b1', '72.eh1.b1', '72.ek1.b1', '72.em1.b1', '72.ep1.b1', '72.fe1.b1'], 'contains': ['288.l1.a1', '288.s1.b1', '432.w1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6360, -1, 4711, -1, 4302, -1, 4769, -1], 'generators': [793511, 887131, 622537], 'label': '1728.46354.144.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.cs1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336890
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '6.u1.a1'], 'contains': ['24.h1.a1', '24.n1.a1', '24.q1.a1', '24.bl1.a1', '24.bm1.a1', '36.x1.a1', '36.z1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1540, -1, 6940, -1, 8078, -1, 8274, -1], 'generators': [46999, 622105, 793169, 835777, 887131, 622537], 'label': '1728.46354.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 264336891
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '72.i1.a1', '72.dw1.a1', '72.en1.a1', '72.en1.a2', '72.eq1.a1', '72.eq1.a2', '72.ff1.a1'], 'contains': ['288.m1.a1', '288.t1.a1', '432.w1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6602, -1, 3002, -1, 3663, -1, 3544, -1], 'generators': [46999, 887131, 47089], 'label': '1728.46354.144.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.ct1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336892
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.b1', '72.i1.a1', '72.dw1.b1', '72.en1.b1', '72.en1.b2', '72.eq1.b1', '72.eq1.b2', '72.ff1.b1'], 'contains': ['288.m1.a1', '288.t1.b1', '432.w1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6602, -1, 3592, -1, 3663, -1, 3318, -1], 'generators': [793511, 887131, 47089], 'label': '1728.46354.144.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.ct1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336893
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.j1.a1', '72.ds1.a1', '72.ej1.a1', '72.ej1.b1', '72.er1.a1', '72.er1.b1', '72.ez1.a1'], 'contains': ['288.k1.a1', '288.v1.a1', '432.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7080, -1, 4993, -1, 4675, -1, 5286, -1], 'generators': [1651771, 887131, 622105], 'label': '1728.46354.144.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '144.cu1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336894
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.k1.a1', '72.dt1.a1', '72.ek1.a1', '72.ek1.b1', '72.es1.a1', '72.es1.b1', '72.fc1.a1'], 'contains': ['288.l1.a1', '288.w1.a1', '432.x1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7109, -1, 5310, -1, 4647, -1, 5435, -1], 'generators': [1651771, 887131, 622537], 'label': '1728.46354.144.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.cv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336895
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.cw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '72.l1.a1', '72.dx1.a1', '72.el1.a1', '72.el1.b1', '72.et1.a1', '72.et1.b1', '72.fh1.a1'], 'contains': ['288.k1.a1', '288.y1.a1', '288.bf1.a1', '432.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5718, -1, 3834, -1, 4238, -1, 4266, -1], 'generators': [1634131, 887131, 622105], 'label': '1728.46354.144.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '144.cw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336896
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '144.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '72.m1.a1', '72.dy1.a1', '72.em1.a1', '72.em1.b1', '72.eu1.a1', '72.eu1.b1', '72.fi1.a1'], 'contains': ['288.l1.a1', '288.z1.a1', '288.bg1.a1', '432.y1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5831, -1, 4092, -1, 4159, -1, 4427, -1], 'generators': [1634131, 887131, 622537], 'label': '1728.46354.144.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.cx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336897
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '72.n1.a1', '72.dz1.a1', '72.en1.a1', '72.en1.b1', '72.ev1.a1', '72.ev1.b1', '72.fj1.a1'], 'contains': ['288.m1.a1', '288.ba1.a1', '288.bh1.a2', '432.y1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6075, -1, 3053, -1, 3599, -1, 3505, -1], 'generators': [1634131, 887131, 47089], 'label': '1728.46354.144.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.cy1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336898
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '72.n1.a1', '72.dz1.a2', '72.en1.a2', '72.en1.b2', '72.ev1.a2', '72.ev1.b2', '72.fj1.a2'], 'contains': ['288.m1.a1', '288.ba1.a2', '288.bh1.a1', '432.y1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6075, -1, 3199, -1, 3599, -1, 3567, -1], 'generators': [1634131, 887131, 1197949], 'label': '1728.46354.144.cy1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.cy1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336899
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.cz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1.a1', '72.o1.a1', '72.ea1.a1', '72.ef1.a1', '72.ef1.b1', '72.er1.a1', '72.er1.b1', '72.fk1.a1'], 'contains': ['288.k1.a1', '288.bb1.a1', '432.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6747, -1, 4920, -1, 5217, -1, 5621, -1], 'generators': [1675405, 887131, 622105], 'label': '1728.46354.144.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '144.cz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336900
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.da1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1.a1', '72.p1.a1', '72.eb1.a1', '72.eh1.a1', '72.eh1.b1', '72.es1.a1', '72.es1.b1', '72.fl1.a1'], 'contains': ['288.l1.a1', '288.bc1.a1', '432.z1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6775, -1, 5298, -1, 5035, -1, 5679, -1], 'generators': [1675405, 887131, 622537], 'label': '1728.46354.144.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.da1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.da1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336901
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '6.u1.a1'], 'contains': ['24.h1.a1', '24.p1.a1', '24.s1.a1', '36.y1.a1', '36.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2574, -1, 8157, -1, 7523, -1, 7540, -1], 'generators': [46999, 622105, 887131, 811801, 622537, 793169], 'label': '1728.46354.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336902
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.db1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '72.q1.a1', '72.dx1.a1', '72.eo1.a1', '72.eo1.b1', '72.ew1.a1', '72.ew1.b1', '72.fh1.a1'], 'contains': ['288.k1.a1', '288.bf1.a1', '432.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5702, -1, 3782, -1, 4097, -1, 3796, -1], 'generators': [1656811, 887131, 622105], 'label': '1728.46354.144.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '144.db1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336903
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.dc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '72.r1.a1', '72.dy1.a1', '72.ep1.a1', '72.ep1.b1', '72.ex1.a1', '72.ex1.b1', '72.fi1.a1'], 'contains': ['288.l1.a1', '288.bg1.a1', '432.ba1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5762, -1, 4104, -1, 4058, -1, 4022, -1], 'generators': [1656811, 887131, 622537], 'label': '1728.46354.144.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.dc1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336904
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '72.s1.a1', '72.dz1.a1', '72.eq1.a1', '72.eq1.b1', '72.ey1.a1', '72.ey1.b1', '72.fj1.a2'], 'contains': ['288.m1.a1', '288.bh1.a1', '432.ba1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6380, -1, 3456, -1, 3580, -1, 2958, -1], 'generators': [1656811, 887131, 1197949], 'label': '1728.46354.144.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.dd1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336905
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '72.s1.a1', '72.dz1.a2', '72.eq1.a2', '72.eq1.b2', '72.ey1.a2', '72.ey1.b2', '72.fj1.a1'], 'contains': ['288.m1.a1', '288.bh1.a2', '432.ba1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6380, -1, 3467, -1, 3580, -1, 3028, -1], 'generators': [1656811, 887131, 47089], 'label': '1728.46354.144.dd1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.dd1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336906
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.de1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '72.t1.a1', '72.ec1.a1', '72.el1.a1', '72.el1.b1', '72.ew1.a1', '72.ew1.b1', '72.fo1.a1'], 'contains': ['288.k1.a1', '288.bi1.a1', '432.bb1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5817, -1, 3737, -1, 4077, -1, 4006, -1], 'generators': [1633789, 887131, 622105], 'label': '1728.46354.144.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '144.de1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.de1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336907
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.df1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '72.u1.a1', '72.ed1.a1', '72.em1.a1', '72.em1.b1', '72.ex1.a1', '72.ex1.b1', '72.fp1.a1'], 'contains': ['288.l1.a1', '288.bj1.a1', '432.bb1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5943, -1, 4037, -1, 3995, -1, 4283, -1], 'generators': [1633789, 887131, 622537], 'label': '1728.46354.144.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.df1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.df1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336908
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '72.v1.a1', '72.ee1.a1', '72.en1.a1', '72.en1.b2', '72.ey1.a2', '72.ey1.b1', '72.fq1.a1'], 'contains': ['288.m1.a1', '288.bk1.a1', '432.bb1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6719, -1, 3162, -1, 3560, -1, 3295, -1], 'generators': [1633789, 887131, 47089], 'label': '1728.46354.144.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.dg1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336909
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '72.v1.a1', '72.ee1.a2', '72.en1.a2', '72.en1.b1', '72.ey1.a1', '72.ey1.b2', '72.fq1.a2'], 'contains': ['288.m1.a1', '288.bk1.a2', '432.bb1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6719, -1, 3112, -1, 3560, -1, 3279, -1], 'generators': [1633789, 887131, 1197949], 'label': '1728.46354.144.dg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.dg1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336910
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '72.x1.a1', '72.du1.b1', '72.eg1.a1', '72.er1.a1', '72.et1.a1', '72.ew1.a1', '72.fd1.a1'], 'contains': ['288.k1.a1', '432.bc1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6505, -1, 4385, -1, 4180, -1, 4465, -1], 'generators': [70957, 622105, 887131], 'label': '1728.46354.144.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.dh1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336911
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.b1', '72.x1.a1', '72.du1.a1', '72.eg1.b1', '72.er1.b1', '72.et1.b1', '72.ew1.b1', '72.fd1.b1'], 'contains': ['288.k1.a1', '432.bc1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6505, -1, 4350, -1, 4180, -1, 4445, -1], 'generators': [817469, 622105, 887131], 'label': '1728.46354.144.dh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.dh1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336912
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.i1.a1', '24.j1.a1', '24.p1.a1', '24.bs1.a1', '24.bu1.a1', '36.bb1.a1', '36.bg1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2519, -1, 7813, -1, 7571, -1, 7783, -1], 'generators': [1651771, 622105, 622537, 811801, 887131, 793169], 'label': '1728.46354.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336913
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.di1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1.a1', '72.ba1.a1', '72.ea1.a1', '72.eg1.a1', '72.eg1.b1', '72.ej1.a1', '72.ej1.b1', '72.fk1.a1'], 'contains': ['288.k1.a1', '432.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7125, -1, 4810, -1, 4503, -1, 5064, -1], 'generators': [1651447, 622105, 887131], 'label': '1728.46354.144.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '144.di1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.di1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336914
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.dj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1.a1', '72.bc1.a1', '72.ec1.a1', '72.eo1.a1', '72.eo1.b1', '72.et1.a1', '72.et1.b1', '72.fo1.a1'], 'contains': ['288.k1.a1', '432.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5793, -1, 3676, -1, 3757, -1, 3703, -1], 'generators': [1656487, 887131, 622105], 'label': '1728.46354.144.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.ba1.a1', 'old_label': '144.dj1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336915
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '72.be1.a1', '72.dv1.b1', '72.ei1.a1', '72.es1.a1', '72.eu1.a1', '72.ex1.a1', '72.fe1.a1'], 'contains': ['288.l1.a1', '432.bc1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6580, -1, 4682, -1, 4137, -1, 4504, -1], 'generators': [70957, 622537, 887131], 'label': '1728.46354.144.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.dk1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336916
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.b1', '72.be1.a1', '72.dv1.a1', '72.ei1.b1', '72.es1.b1', '72.eu1.b1', '72.ex1.b1', '72.fe1.b1'], 'contains': ['288.l1.a1', '432.bc1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6580, -1, 4444, -1, 4137, -1, 4484, -1], 'generators': [817469, 622537, 887131], 'label': '1728.46354.144.dk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.dk1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336917
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '144.dl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1.a1', '72.bh1.a1', '72.eb1.a1', '72.ei1.a1', '72.ei1.b1', '72.ek1.a1', '72.ek1.b1', '72.fl1.a1'], 'contains': ['288.l1.a1', '432.bd1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7177, -1, 5075, -1, 4471, -1, 5084, -1], 'generators': [1651447, 887131, 622537], 'label': '1728.46354.144.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.dl1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336918
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '144.dm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1.a1', '72.bj1.a1', '72.ed1.a1', '72.ep1.a1', '72.ep1.b1', '72.eu1.a1', '72.eu1.b1', '72.fp1.a1'], 'contains': ['288.l1.a1', '432.be1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5891, -1, 3901, -1, 3694, -1, 3924, -1], 'generators': [1656487, 887131, 622537], 'label': '1728.46354.144.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.dm1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336919
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '72.bk1.a1', '72.dw1.b1', '72.ev1.a1', '72.ev1.a2', '72.ey1.a1', '72.ey1.a2', '72.ff1.a1'], 'contains': ['288.m1.a1', '432.bc1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6806, -1, 3311, -1, 3539, -1, 2783, -1], 'generators': [70957, 47089, 887131], 'label': '1728.46354.144.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.dn1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336920
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.b1', '72.bk1.a1', '72.dw1.a1', '72.ev1.b1', '72.ev1.b2', '72.ey1.b1', '72.ey1.b2', '72.ff1.b1'], 'contains': ['288.m1.a1', '432.bc1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6806, -1, 2966, -1, 3539, -1, 2976, -1], 'generators': [817469, 47089, 887131], 'label': '1728.46354.144.dn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '144.dn1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336921
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1.a1', '72.bl1.a1', '72.ee1.a1', '72.eq1.a1', '72.eq1.b2', '72.ev1.a2', '72.ev1.b1', '72.fq1.a2'], 'contains': ['288.m1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6002, -1, 3149, -1, 3367, -1, 2865, -1], 'generators': [1656487, 887131, 1197949], 'label': '1728.46354.144.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.do1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336922
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1.a1', '72.bl1.a1', '72.ee1.a2', '72.eq1.a2', '72.eq1.b1', '72.ev1.a1', '72.ev1.b2', '72.fq1.a1'], 'contains': ['288.m1.a1', '432.be1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6002, -1, 3023, -1, 3367, -1, 2891, -1], 'generators': [1656487, 887131, 47089], 'label': '1728.46354.144.do1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bc1.a1', 'old_label': '144.do1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336923
    {'ambient': '1728.46354', 'aut_centralizer_order': 12, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 36, 'centralizer': '144.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.k1.a1', '6.o1.a1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.o1.a1', '24.ct1.a1', '24.ct1.b1', '36.bc1.a1', '36.bh1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2450, -1, 7387, -1, 6617, -1, 6584, -1], 'generators': [70957, 622537, 887131, 1651771, 793169, 622105], 'label': '1728.46354.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.v1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 264336924
    {'ambient': '1728.46354', 'aut_centralizer_order': 288, 'aut_label': '144.dp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.ch1.a1', '48.ci1.a1', '72.bm1.a1', '72.ff1.a1', '72.ff1.b1', '72.fj1.a1', '72.fj1.a2', '72.fq1.a1', '72.fq1.a2'], 'contains': ['288.m1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8470, -1, 1351, -1, 2760, -1, 1832, -1], 'generators': [887131, 70633, 47089], 'label': '1728.46354.144.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '144.dp1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264336925
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.dq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.cg1.a1', '48.ci1.a1', '72.bn1.a1', '72.fb1.a1', '72.fs1.a1'], 'contains': ['432.a1.a1', '576.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9598, -1, 424, -1, 354, -1, 423, -1], 'generators': [766291, 887131, 70633], 'label': '1728.46354.144.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.dq1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336926
    {'ambient': '1728.46354', 'aut_centralizer_order': 144, 'aut_label': '144.dr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.cf1.a1', '48.ci1.a1', '72.bo1.a1', '72.fn1.a1', '72.ft1.a1'], 'contains': ['432.a1.a1', '576.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9821, -1, 832, -1, 929, -1, 1259, -1], 'generators': [767155, 887131, 70633], 'label': '1728.46354.144.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '144.dr1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336927
    {'ambient': '1728.46354', 'aut_centralizer_order': 72, 'aut_label': '144.ds1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.a1', '48.cg1.a1', '48.ch1.a1', '48.ci1.a1', '72.bp1.a1', '72.fu1.a1', '72.fu1.a2'], 'contains': ['432.a1.a1', '576.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9942, -1, 205, -1, 267, -1, 287, -1], 'generators': [1342135, 887131, 70633], 'label': '1728.46354.144.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '144.ds1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264336928
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1.a1', '48.ck1.a1', '72.bq1.a1', '72.dj1.a1', '72.ef1.a1'], 'contains': ['288.n1.a1', '288.r1.a1', '288.bb1.a1', '432.bf1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4818, -1, 8598, -1, 8273, -1, 7587, -1], 'generators': [46999, 1674451, 622105], 'label': '1728.46354.144.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.dt1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336929
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1.b1', '48.ck1.b1', '72.bq1.a1', '72.dj1.a1', '72.ef1.b1'], 'contains': ['288.n1.a1', '288.r1.b1', '288.bb1.a1', '432.bf1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4818, -1, 8576, -1, 8273, -1, 7617, -1], 'generators': [793511, 1674451, 622105], 'label': '1728.46354.144.dt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.dt1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336930
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ec1.a1', '48.cj1.a1', '48.cl1.a1', '72.br1.a1'], 'contains': ['288.o1.a1', '288.u1.a1', '288.bd1.a1', '432.bf1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9372, -1, 1191, -1, 1558, -1, 1554, -1], 'generators': [46999, 1674451, 1341703], 'label': '1728.46354.144.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '144.du1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336931
    {'ambient': '1728.46354', 'aut_centralizer_order': 24, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ec1.b1', '48.cj1.b1', '48.cl1.b1', '72.br1.a1'], 'contains': ['288.o1.a1', '288.u1.b1', '288.bd1.a1', '432.bf1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9372, -1, 1500, -1, 1558, -1, 1601, -1], 'generators': [793511, 1674451, 1341703], 'label': '1728.46354.144.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1.a1', 'old_label': '144.du1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336932
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1.a1', '48.cl1.a1', '72.by1.a1', '72.dk1.a1', '72.eh1.a1'], 'contains': ['288.q1.a1', '288.s1.a1', '288.bc1.a1', '432.bf1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4846, -1, 8302, -1, 7298, -1, 8634, -1], 'generators': [46999, 1674451, 622537], 'label': '1728.46354.144.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '144.dv1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336933
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1.b1', '48.cl1.b1', '72.by1.a1', '72.dk1.a1', '72.eh1.b1'], 'contains': ['288.q1.a1', '288.s1.b1', '288.bc1.a1', '432.bf1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4846, -1, 8274, -1, 7298, -1, 8699, -1], 'generators': [793511, 1674451, 622537], 'label': '1728.46354.144.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '144.dv1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336934
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.i1.a1', '24.l1.a1', '24.n1.a1', '24.bt1.a1', '24.bu1.a1', '36.bd1.a1', '36.bi1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1968, -1, 6682, -1, 7672, -1, 7688, -1], 'generators': [1651771, 622105, 622537, 835777, 887131, 793169], 'label': '1728.46354.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.w1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336935
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.a1', '72.cc1.a1', '72.dj1.a1', '72.ef1.a1'], 'contains': ['288.r1.a1', '288.v1.a1', '288.bb1.a1', '432.bg1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3466, -1, 9816, -1, 8766, -1, 8471, -1], 'generators': [46999, 835273, 622105], 'label': '1728.46354.144.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.dw1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336936
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.b1', '72.cc1.a1', '72.dj1.a1', '72.ef1.b1'], 'contains': ['288.r1.b1', '288.v1.a1', '288.bb1.a1', '432.bg1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3466, -1, 9794, -1, 8766, -1, 8501, -1], 'generators': [793511, 835273, 622105], 'label': '1728.46354.144.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '144.dw1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264336937
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.a1', '72.cd1.a1', '72.dk1.a1', '72.eh1.a1'], 'contains': ['288.s1.a1', '288.w1.a1', '288.bc1.a1', '432.bg1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3486, -1, 9202, -1, 8245, -1, 8956, -1], 'generators': [46999, 835273, 622537], 'label': '1728.46354.144.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '144.dx1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336938
    {'ambient': '1728.46354', 'aut_centralizer_order': 48, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.b1', '72.cd1.a1', '72.dk1.a1', '72.eh1.b1'], 'contains': ['288.s1.b1', '288.w1.a1', '288.bc1.a1', '432.bg1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3486, -1, 9172, -1, 8245, -1, 8972, -1], 'generators': [793511, 835273, 622537], 'label': '1728.46354.144.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '144.dx1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336939
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '48.cp1.a1', '72.ce1.a1', '72.dl1.a1', '72.el1.a1'], 'contains': ['288.r1.a1', '288.y1.a1', '288.bi1.a1', '432.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4008, -1, 8782, -1, 7354, -1, 7138, -1], 'generators': [46999, 1634131, 622105], 'label': '1728.46354.144.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '144.dy1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336940
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.b1', '48.cp1.b1', '72.ce1.a1', '72.dl1.a1', '72.el1.b1'], 'contains': ['288.r1.b1', '288.y1.a1', '288.bi1.a1', '432.bh1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4008, -1, 8734, -1, 7354, -1, 7173, -1], 'generators': [793511, 1634131, 622105], 'label': '1728.46354.144.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '144.dy1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336941
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '48.cq1.a1', '72.cf1.a1', '72.dm1.a1', '72.em1.a1'], 'contains': ['288.s1.a1', '288.z1.a1', '288.bj1.a1', '432.bh1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4054, -1, 8382, -1, 6916, -1, 7742, -1], 'generators': [46999, 1634131, 622537], 'label': '1728.46354.144.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '144.dz1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336942
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.b1', '48.cq1.b1', '72.cf1.a1', '72.dm1.a1', '72.em1.b1'], 'contains': ['288.s1.b1', '288.z1.a1', '288.bj1.a1', '432.bh1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4054, -1, 8358, -1, 6916, -1, 7758, -1], 'generators': [793511, 1634131, 622537], 'label': '1728.46354.144.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '144.dz1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336943
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '48.cr1.a1', '72.cg1.a1', '72.dn1.a1', '72.en1.a1'], 'contains': ['288.t1.a1', '288.ba1.a1', '288.bk1.a1', '432.bh1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5056, -1, 5836, -1, 5634, -1, 6522, -1], 'generators': [46999, 1634131, 47089], 'label': '1728.46354.144.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ea1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336944
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '48.cr1.a2', '72.cg1.a1', '72.dn1.a2', '72.en1.a2'], 'contains': ['288.t1.a1', '288.ba1.a2', '288.bk1.a2', '432.bh1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5056, -1, 5891, -1, 5634, -1, 6538, -1], 'generators': [46999, 1634131, 1197949], 'label': '1728.46354.144.ea1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ea1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336945
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.k1.a1', '6.q1.a1'], 'contains': ['24.i1.a1', '24.m1.a1', '24.s1.a1', '24.ch1.a1', '36.be1.a1', '36.bj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2211, -1, 7909, -1, 7476, -1, 7646, -1], 'generators': [812125, 622105, 622537, 1651771, 887131, 1633643], 'label': '1728.46354.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.x1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336946
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.b1', '48.cr1.b1', '72.cg1.a1', '72.dn1.a1', '72.en1.b1'], 'contains': ['288.t1.b1', '288.ba1.a1', '288.bk1.a2', '432.bh1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5056, -1, 5879, -1, 5634, -1, 6554, -1], 'generators': [793511, 1634131, 47089], 'label': '1728.46354.144.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ea1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336947
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.b1', '48.cr1.b2', '72.cg1.a1', '72.dn1.a2', '72.en1.b2'], 'contains': ['288.t1.b1', '288.ba1.a2', '288.bk1.a1', '432.bh1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5056, -1, 5867, -1, 5634, -1, 6570, -1], 'generators': [793511, 1634131, 1197949], 'label': '1728.46354.144.ea1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ea1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336948
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.ch1.a1', '72.dl1.a1', '72.el1.a1'], 'contains': ['288.r1.a1', '288.bf1.a1', '288.bi1.a1', '432.bi1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2335, -1, 9778, -1, 8141, -1, 8059, -1], 'generators': [46999, 793657, 622105], 'label': '1728.46354.144.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '144.eb1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336949
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.b1', '72.ch1.a1', '72.dl1.a1', '72.el1.b1'], 'contains': ['288.r1.b1', '288.bf1.a1', '288.bi1.a1', '432.bi1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2335, -1, 9767, -1, 8141, -1, 8075, -1], 'generators': [793511, 793657, 622105], 'label': '1728.46354.144.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '144.eb1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336950
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.ci1.a1', '72.dm1.a1', '72.em1.a1'], 'contains': ['288.s1.a1', '288.bg1.a1', '288.bj1.a1', '432.bi1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2624, -1, 9402, -1, 7676, -1, 8524, -1], 'generators': [46999, 793657, 622537], 'label': '1728.46354.144.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '144.ec1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336951
    {'ambient': '1728.46354', 'aut_centralizer_order': 16, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.b1', '72.ci1.a1', '72.dm1.a1', '72.em1.b1'], 'contains': ['288.s1.b1', '288.bg1.a1', '288.bj1.a1', '432.bi1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2624, -1, 9292, -1, 7676, -1, 8601, -1], 'generators': [793511, 793657, 622537], 'label': '1728.46354.144.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1.a1', 'old_label': '144.ec1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336952
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.cj1.a1', '72.dn1.a1', '72.en1.a2'], 'contains': ['288.t1.a1', '288.bh1.a1', '288.bk1.a2', '432.bi1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2839, -1, 7421, -1, 6897, -1, 7383, -1], 'generators': [46999, 793657, 1197949], 'label': '1728.46354.144.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ed1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336953
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.cj1.a1', '72.dn1.a2', '72.en1.a1'], 'contains': ['288.t1.a1', '288.bh1.a2', '288.bk1.a1', '432.bi1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2839, -1, 7382, -1, 6897, -1, 7399, -1], 'generators': [46999, 793657, 47089], 'label': '1728.46354.144.ed1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ed1.a2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336954
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.b1', '72.cj1.a1', '72.dn1.a1', '72.en1.b2'], 'contains': ['288.t1.b1', '288.bh1.a1', '288.bk1.a1', '432.bi1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2839, -1, 7397, -1, 6897, -1, 7431, -1], 'generators': [793511, 793657, 1197949], 'label': '1728.46354.144.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ed1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336955
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.b1', '72.cj1.a1', '72.dn1.a2', '72.en1.b1'], 'contains': ['288.t1.b1', '288.bh1.a2', '288.bk1.a2', '432.bi1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2839, -1, 7314, -1, 6897, -1, 7415, -1], 'generators': [793511, 793657, 47089], 'label': '1728.46354.144.ed1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1.a1', 'old_label': '144.ed1.b2', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336956
    {'ambient': '1728.46354', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.j1.a1', '6.q1.a1'], 'contains': ['24.i1.a1', '24.q1.a1', '24.t1.a1', '36.bf1.a1', '36.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2004, -1, 6617, -1, 6788, -1, 6954, -1], 'generators': [834823, 622105, 622537, 1651771, 793169, 887131], 'label': '1728.46354.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 264336957
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eh1.a1', '48.cp1.a1', '48.cq1.a1', '48.cr1.a1', '48.cr1.a2', '72.co1.a1'], 'contains': ['288.u1.a1', '288.x1.a1', '288.bl1.a1', '432.bh1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9012, -1, 643, -1, 1091, -1, 834, -1], 'generators': [46999, 1634131, 1341703], 'label': '1728.46354.144.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.co1.a1', 'old_label': '144.ee1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336958
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '432.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eh1.b1', '48.cp1.b1', '48.cq1.b1', '48.cr1.b1', '48.cr1.b2', '72.co1.a1'], 'contains': ['288.u1.b1', '288.x1.a1', '288.bl1.a1', '432.bh1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9012, -1, 491, -1, 1091, -1, 850, -1], 'generators': [793511, 1634131, 1341703], 'label': '1728.46354.144.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.co1.a1', 'old_label': '144.ee1.b1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336959
    {'ambient': '1728.46354', 'aut_centralizer_order': 1728, 'aut_label': '192.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': ['9.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.h1.a1', '96.i1.a1', '96.k1.a1', '96.n1.a1', '96.n1.b1', '96.r1.a1', '96.v1.a1', '96.w1.a1', '96.ba1.a1', '96.bb1.a1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3680, 6271, 9441, 4444, 7558, 5911, 8043, 4895], 'generators': [622537, 622105], 'label': '1728.46354.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.d1.a1', '96.a1.a1'], 'normal_contains': ['576.a1.a1', '576.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1728.46354', 'quotient_action_image': '4.2', 'quotient_action_kernel': '48.48', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336960
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '64.a1.a1', '96.b1.a1', '96.j1.a1', '96.o1.a1', '96.o1.b1', '96.s1.a1', '96.x1.a1', '96.bc1.a1'], 'contains': ['576.a1.a1', '576.d1.a1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9575, -1, 1042, -1, 1323, -1, 1175, -1], 'generators': [1341703, 622105], 'label': '1728.46354.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '192.b1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336961
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.a1', '64.a1.a1', '96.c1.a1', '96.y1.a1', '96.bd1.a1'], 'contains': ['576.a1.a1', '576.f1.a1', '576.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9698, -1, 875, -1, 1195, -1, 1272, -1], 'generators': [767155, 622105], 'label': '1728.46354.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '192.c1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336962
    {'ambient': '1728.46354', 'aut_centralizer_order': 432, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '64.a1.a1', '96.d1.a1', '96.l1.a1', '96.p1.a1', '96.p1.b1', '96.t1.a1', '96.z1.a1', '96.be1.a1'], 'contains': ['576.b1.a1', '576.d1.a1', '576.f1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9077, -1, 907, -1, 1301, -1, 1241, -1], 'generators': [1341703, 622537], 'label': '1728.46354.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '192.d1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336963
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1.a1', '64.a1.a1', '96.e1.a1', '96.m1.a1', '96.bf1.a1'], 'contains': ['576.b1.a1', '576.e1.a1', '576.g1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9441, -1, 708, -1, 867, -1, 1053, -1], 'generators': [766291, 622537], 'label': '1728.46354.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '192.e1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336964
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1.a1', '64.a1.a1', '96.f1.a1', '96.q1.a1', '96.q1.b1', '96.u1.a1', '96.u1.a2', '96.bg1.a1', '96.bg1.a2'], 'contains': ['576.c1.a1', '576.d1.a1', '576.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9559, -1, 551, -1, 1119, -1, 783, -1], 'generators': [1341703, 47089], 'label': '1728.46354.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '192.f1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336965
    {'ambient': '1728.46354', 'aut_centralizer_order': 216, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1.a1', '64.a1.a1', '96.g1.a1', '96.bh1.a1', '96.bh1.a2'], 'contains': ['576.c1.a1', '576.e1.a1', '576.f1.a1', '576.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9682, -1, 354, -1, 903, -1, 921, -1], 'generators': [766291, 47089], 'label': '1728.46354.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.f1.a1', 'old_label': '192.g1.a1', 'projective_image': '1728.46354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336966
    {'ambient': '1728.46354', 'aut_centralizer_order': 1152, 'aut_label': '216.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.bm1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '108.bc1.a1', '108.bd1.a1', '108.be1.a1', '108.bf1.a1', '108.bg1.a1', '108.bh1.a1', '108.bi1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.u1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6043, 4335, 4808, 5707, 3815, 4782, 3989, 4648], 'generators': [793169, 887131, 70633], 'label': '1728.46354.216.a1.a1', 'mobius_quo': 1, 'mobius_sub': 216, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1'], 'normal_contains': ['432.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264336967
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1', '6.bb1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.q1.a1', '24.by1.a1', '24.bz1.a1', '36.bl1.a1', '36.bm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2119, -1, 7844, -1, 8186, -1, 8226, -1], 'generators': [834823, 622105, 622537, 1634131, 887131, 793169], 'label': '1728.46354.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336968
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.bc1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.e1.a1', '432.m1.a1', '432.v1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3923, -1, 7488, -1, 6855, -1, 7072, -1], 'generators': [1674451, 793169, 887131], 'label': '1728.46354.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336969
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.h1.a1', '72.i1.a1', '108.a1.a1', '108.g1.a1', '108.h1.a1', '108.i1.a1', '108.j1.a1', '108.k1.a1', '108.bd1.a1'], 'contains': ['432.b1.a1', '432.d1.a1', '432.n1.a1', '432.w1.a1', '432.w1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2457, -1, 6863, -1, 6658, -1, 6719, -1], 'generators': [46999, 793169, 887131], 'label': '1728.46354.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.c1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336970
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.cl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.k1.a1', '108.g1.a1', '108.l1.a1', '108.m1.a1', '108.n1.a1', '108.o1.a1', '108.p1.a1', '108.bc1.a1'], 'contains': ['432.b1.a1', '432.e1.a1', '432.o1.a1', '432.x1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1764, -1, 6367, -1, 6147, -1, 6683, -1], 'generators': [1651771, 793169, 887131], 'label': '1728.46354.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.d1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336971
    {'ambient': '1728.46354', 'aut_centralizer_order': 128, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '54.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.m1.a1', '72.n1.a1', '108.b1.a1', '108.h1.a1', '108.l1.a1', '108.q1.a1', '108.r1.a1', '108.s1.a1', '108.be1.a1'], 'contains': ['432.b1.a1', '432.f1.a1', '432.h1.a1', '432.p1.a1', '432.y1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4079, -1, 7475, -1, 6599, -1, 6770, -1], 'generators': [1634131, 793169, 887131], 'label': '1728.46354.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336972
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.a1', '72.p1.a1', '108.a1.a1', '108.m1.a1', '108.q1.a1', '108.t1.a1', '108.u1.a1', '108.v1.a1', '108.bf1.a1'], 'contains': ['432.b1.a1', '432.g1.a1', '432.q1.a1', '432.z1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2834, -1, 7626, -1, 6876, -1, 7091, -1], 'generators': [1675405, 793169, 887131], 'label': '1728.46354.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336973
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.r1.a1', '72.s1.a1', '108.c1.a1', '108.i1.a1', '108.n1.a1', '108.t1.a1', '108.w1.a1', '108.x1.a1', '108.be1.a1'], 'contains': ['432.b1.a1', '432.h1.a1', '432.r1.a1', '432.ba1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2931, -1, 6337, -1, 6088, -1, 6648, -1], 'generators': [1656811, 793169, 887131], 'label': '1728.46354.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.g1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336974
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '72.u1.a1', '72.v1.a1', '108.d1.a1', '108.h1.a1', '108.o1.a1', '108.u1.a1', '108.w1.a1', '108.y1.a1', '108.bg1.a1'], 'contains': ['432.b1.a1', '432.i1.a1', '432.s1.a1', '432.bb1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2156, -1, 7456, -1, 6577, -1, 6701, -1], 'generators': [1633789, 793169, 887131], 'label': '1728.46354.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336975
    {'ambient': '1728.46354', 'aut_centralizer_order': 384, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1.a1', '72.bd1.a1', '108.b1.a1', '108.j1.a1', '108.n1.a1', '108.u1.a1', '108.z1.a1', '108.ba1.a1', '108.bh1.a1'], 'contains': ['432.b1.a1', '432.j1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1517, -1, 6904, -1, 6787, -1, 7115, -1], 'generators': [835777, 887131], 'label': '1728.46354.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.i1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336976
    {'ambient': '1728.46354', 'aut_centralizer_order': 576, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1.a1', '72.be1.a1', '72.bk1.a1', '108.e1.a1', '108.m1.a1', '108.r1.a1', '108.w1.a1', '108.z1.a1', '108.bb1.a1', '108.bd1.a1'], 'contains': ['432.b1.a1', '432.bc1.a1', '432.bc1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2400, -1, 7011, -1, 5700, -1, 6239, -1], 'generators': [70957, 793169], 'label': '1728.46354.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.j1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336977
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1.a1', '72.bf1.a1', '108.c1.a1', '108.k1.a1', '108.l1.a1', '108.v1.a1', '108.y1.a1', '108.bb1.a1', '108.bh1.a1'], 'contains': ['432.b1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2631, -1, 7863, -1, 6236, -1, 6825, -1], 'generators': [811801, 887131], 'label': '1728.46354.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.k1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336978
    {'ambient': '1728.46354', 'aut_centralizer_order': 8, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.t1.a1'], 'contains': ['24.j1.a1', '24.o1.a1', '24.t1.a1', '24.cu1.a1', '24.cu1.b1', '36.bn1.a1', '36.bp1.a1', '36.br1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4554, -1, 7311, -1, 5812, -1, 5774, -1], 'generators': [70957, 622105, 622537, 1634131, 793169, 887131], 'label': '1728.46354.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 264336979
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1.a1', '72.bg1.a1', '108.d1.a1', '108.j1.a1', '108.p1.a1', '108.q1.a1', '108.x1.a1', '108.bb1.a1', '108.bi1.a1'], 'contains': ['432.b1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1288, -1, 6747, -1, 6750, -1, 7048, -1], 'generators': [834823, 887131], 'label': '1728.46354.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.l1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336980
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1.a1', '72.bh1.a1', '108.e1.a1', '108.g1.a1', '108.s1.a1', '108.x1.a1', '108.y1.a1', '108.ba1.a1', '108.bf1.a1'], 'contains': ['432.b1.a1', '432.bd1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4417, -1, 6140, -1, 5829, -1, 6624, -1], 'generators': [1651447, 793169], 'label': '1728.46354.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.m1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336981
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1.a1', '72.bi1.a1', '108.f1.a1', '108.k1.a1', '108.o1.a1', '108.s1.a1', '108.t1.a1', '108.z1.a1', '108.bi1.a1'], 'contains': ['432.b1.a1', '432.t1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2989, -1, 8136, -1, 6273, -1, 6794, -1], 'generators': [812125, 887131], 'label': '1728.46354.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.n1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336982
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1.a1', '72.bj1.a1', '72.bl1.a1', '108.f1.a1', '108.i1.a1', '108.p1.a1', '108.r1.a1', '108.v1.a1', '108.ba1.a1', '108.bg1.a1'], 'contains': ['432.b1.a1', '432.be1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4360, -1, 6088, -1, 5736, -1, 6309, -1], 'generators': [1656487, 793169], 'label': '1728.46354.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.o1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336983
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.a1', '72.br1.a1', '72.by1.a1', '108.a1.a1', '108.bj1.a1', '108.bk1.a1'], 'contains': ['432.c1.a1', '432.d1.a1', '432.g1.a1', '432.bf1.a1', '432.bf1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4001, -1, 8072, -1, 7277, -1, 7532, -1], 'generators': [46999, 1674451, 793169], 'label': '1728.46354.216.p1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.p1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336984
    {'ambient': '1728.46354', 'aut_centralizer_order': 192, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bs1.a1', '72.bt1.a1', '72.bz1.a1', '108.b1.a1', '108.bj1.a1'], 'contains': ['432.c1.a1', '432.f1.a1', '432.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4517, -1, 7142, -1, 6815, -1, 7205, -1], 'generators': [1674451, 835777], 'label': '1728.46354.216.q1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '216.q1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336985
    {'ambient': '1728.46354', 'aut_centralizer_order': 64, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1.a1', '72.ca1.a1', '108.b1.a1', '108.c1.a1', '108.bk1.a1'], 'contains': ['432.c1.a1', '432.h1.a1', '432.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3322, -1, 8102, -1, 7739, -1, 7987, -1], 'generators': [1674451, 1674955], 'label': '1728.46354.216.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.r1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336986
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1.a1', '72.bw1.a1', '72.bx1.a1', '72.cb1.a1', '108.d1.a1', '108.bj1.a1', '108.bk1.a1'], 'contains': ['432.c1.a1', '432.i1.a1', '432.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2191, -1, 7252, -1, 7021, -1, 7221, -1], 'generators': [834823, 1674451], 'label': '1728.46354.216.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.s1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264336987
    {'ambient': '1728.46354', 'aut_centralizer_order': 96, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.a1', '72.cd1.a1', '108.a1.a1', '108.bl1.a1', '108.bm1.a1'], 'contains': ['432.d1.a1', '432.e1.a1', '432.g1.a1', '432.bg1.a1', '432.bg1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [753, -1, 9543, -1, 8224, -1, 8447, -1], 'generators': [46999, 835273, 793169], 'label': '1728.46354.216.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.t1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264336988
    {'ambient': '1728.46354', 'aut_centralizer_order': 32, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ce1.a1', '72.cf1.a1', '72.cg1.a1', '72.co1.a1', '108.h1.a1', '108.bj1.a1', '108.bl1.a1'], 'contains': ['432.d1.a1', '432.f1.a1', '432.i1.a1', '432.bh1.a1', '432.bh1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3540, -1, 8155, -1, 6962, -1, 7156, -1], 'generators': [46999, 1634131, 793169], 'label': '1728.46354.216.u1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.u1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}