Abstract group data - 1728.47489

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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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 12, 4, 6, 4], 'aut_gens': [[6391486216, 325, 51609948, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040], [211604972, 458, 46470498480, 435, 6227025840, 83467440, 46670803200, 32732869680, 6314117040], [6238351379, 458, 32667264348, 348, 6234641280, 7625520, 32772781440, 13945559040, 6314117040], [171683132, 325, 46510410240, 435, 6227025840, 83467440, 46670803200, 20801370240, 6314117040], [32655939256, 458, 25949912115, 348, 87091200, 6234641280, 46594961280, 20761458480, 6314117040], [6354392339, 458, 20600697948, 348, 6234641280, 87091200, 20761458480, 40443787440, 6314117040], [32695851452, 325, 25986200115, 348, 87091200, 6234641280, 46670803200, 32732869680, 6314117040]], 'aut_group': None, 'aut_hash': 5245665785324382618, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 13824, 'aut_permdeg': 74, 'aut_perms': [95593370222048201658197174698030093496432455729736239481069906208113321259067628591908845367405063689874373, 321153099706613643631047890708067017479137864270637641727489616148145915848731539531378746952509038583613857, 144580708142233766189053431697175243867775773744454197487030317515417056489535111081811117472042025758828664, 56912994490689234335095274005539205362818448925135551996555778562190084837540102671236000379214425651121948, 71105409729367972161169721720051873433424203819175573988257818177147958635357971488329572515252629948495414, 137698588937595558944510409000237651321476787086301569312710613796208525576812245063963103194422912067720814], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 1, 1], [2, 72, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 32, 3, 1], [3, 32, 6, 1], [4, 6, 2, 1], [4, 36, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 2, 1], [6, 12, 1, 1], [6, 12, 2, 3], [6, 12, 4, 1], [6, 32, 3, 1], [6, 32, 6, 1], [6, 72, 2, 1], [8, 72, 2, 1], [12, 6, 4, 1], [12, 12, 2, 1], [12, 12, 4, 1], [12, 36, 4, 1], [24, 72, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_2^4:\\He_3.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '3456.gu', 'autcentquo_hash': 3056348276295266572, 'autcentquo_nilpotent': False, 'autcentquo_order': 3456, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2.(C_2^2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 12, 1], [2, 72, 1], [3, 1, 2], [3, 2, 3], [3, 32, 9], [4, 6, 2], [4, 36, 2], [6, 1, 2], [6, 2, 3], [6, 6, 2], [6, 12, 11], [6, 32, 9], [6, 72, 2], [8, 72, 2], [12, 6, 4], [12, 12, 6], [12, 36, 4], [24, 72, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '288.1036', 'commutator_count': 2, 'commutator_label': '288.987', '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': 47489, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['576.8487', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 1, 1], [2, 72, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 32, 1, 3], [3, 32, 2, 3], [4, 6, 1, 2], [4, 36, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 2, 1], [6, 12, 1, 1], [6, 12, 2, 5], [6, 32, 1, 3], [6, 32, 2, 3], [6, 72, 2, 1], [8, 72, 1, 2], [12, 6, 2, 2], [12, 12, 1, 2], [12, 12, 2, 2], [12, 36, 2, 2], [24, 72, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 152880, 'exponent': 24, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4709', 'hash': 47489, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 3, 3, 2, 2, 2, 2, 1], 'inner_gens': [[6391486216, 325, 160796595, 348, 87091200, 83467440, 46670803200, 32732869680, 6314117040], [6391486216, 325, 51609948, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040], [6267301052, 325, 51609948, 435, 83467440, 87091200, 20801370240, 40367945520, 6314117040], [6391486739, 325, 51609948, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040], [6431408056, 325, 131085708, 435, 7625520, 83467440, 13941935280, 32732869680, 6314117040], [6391486216, 325, 134709468, 435, 7625520, 83467440, 25880682240, 20801370240, 6314117040], [20717182216, 325, 46543719948, 435, 7625520, 6234641280, 13941935280, 32732869680, 6314117040], [211604536, 325, 26074097628, 435, 6310483200, 83467440, 25880682240, 20801370240, 6314117040], [6391486216, 325, 51609948, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040]], 'inner_hash': 1036, 'inner_nilpotent': False, 'inner_order': 288, 'inner_split': True, 'inner_tex': '(C_2\\times C_6):S_4', 'inner_used': [1, 3, 4, 5, 7], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 6], [2, 12], [3, 18], [4, 6], [6, 18], [8, 12]], 'label': '1728.47489', 'linC_count': 48, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 18, 'linQ_dim': 8, 'linQ_dim_count': 18, 'linR_count': 18, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(Q8*C3^2):S4', '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': 30, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 72, 'number_divisions': 47, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 282, 'number_subgroup_classes': 496, 'number_subgroups': 5270, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 91], [3, 296], [4, 84], [6, 584], [8, 144], [12, 240], [24, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 3], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[40285292, 325, 207930675, 435, 7625520, 87091200, 25880682240, 40367945520, 6314117040], [40285292, 458, 207930675, 348, 7625520, 87091200, 25880682240, 40367945520, 6314117040], [211604536, 458, 51609948, 435, 7625520, 83467440, 25877058480, 32772781440, 6314117040], [40285292, 325, 207930675, 348, 7625520, 87091200, 13945559040, 46594961280, 6314117040], [6391486739, 325, 51609600, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040]], 'outer_group': '48.51', 'outer_hash': 51, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [41041, 90720, 24, 131784, 3], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_6', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 6], [3, 6], [4, 6], [6, 10], [8, 6], [12, 7], [16, 4]], 'representations': {'PC': {'code': 197764571922485565482195931318246868713477144030777891374282791073, 'gens': [1, 2, 3, 5, 6, 8], 'pres': [9, 2, 3, 2, 3, 2, 2, 2, 2, 3, 73, 4700, 1307, 74, 6051, 462, 19453, 4865, 6332, 1967, 365, 158, 23335, 11680, 5209, 214]}, 'Perm': {'d': 14, 'gens': [6391486216, 325, 51609948, 435, 7625520, 83467440, 13941935280, 20801370240, 6314117040]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(Q_8\\times C_3^2):S_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 144308262
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 47489, 'group_order': 1728, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 144308273
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 47489, 'group_order': 1728, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 6314117040, 'size': 1}
  • id: 144308284
    {'aut_label': '2B', 'centralizer': '6.f1.a1', 'counter': 3, 'group_counter': 47489, 'group_order': 1728, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 7625520, 'size': 6}
  • id: 144308295
    {'aut_label': '2C', 'centralizer': '12.c1.a1', 'counter': 4, 'group_counter': 47489, 'group_order': 1728, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 13902013440, 'size': 12}
  • id: 144308306
    {'aut_label': '2D', 'centralizer': '72.k1.a1', 'counter': 5, 'group_counter': 47489, 'group_order': 1728, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 13898304572, 'size': 72}
  • id: 144308317
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 47489, 'group_order': 1728, 'label': '3A1', 'order': 3, 'powers': [7, 1], 'representative': 458, 'size': 1}
  • id: 144308328
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 47489, 'group_order': 1728, 'label': '3A-1', 'order': 3, 'powers': [6, 1], 'representative': 325, 'size': 1}
  • id: 144308332
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 47489, 'group_order': 1728, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 435, 'size': 2}
  • id: 144308333
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 9, 'group_counter': 47489, 'group_order': 1728, 'label': '3C1', 'order': 3, 'powers': [10, 1], 'representative': 104, 'size': 2}
  • id: 144308263
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 47489, 'group_order': 1728, 'label': '3C-1', 'order': 3, 'powers': [9, 1], 'representative': 81, 'size': 2}
  • id: 144308264
    {'aut_label': '3D', 'centralizer': '32.a1.a1', 'counter': 11, 'group_counter': 47489, 'group_order': 1728, 'label': '3D', 'order': 3, 'powers': [11, 1], 'representative': 168018480, 'size': 32}
  • id: 144308265
    {'aut_label': '3D', 'centralizer': '32.a1.a1', 'counter': 12, 'group_counter': 47489, 'group_order': 1728, 'label': '3E', 'order': 3, 'powers': [12, 1], 'representative': 168018915, 'size': 32}
  • id: 144308266
    {'aut_label': '3D', 'centralizer': '32.a1.a1', 'counter': 13, 'group_counter': 47489, 'group_order': 1728, 'label': '3F', 'order': 3, 'powers': [13, 1], 'representative': 168018828, 'size': 32}
  • id: 144308267
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 14, 'group_counter': 47489, 'group_order': 1728, 'label': '3G1', 'order': 3, 'powers': [15, 1], 'representative': 168018584, 'size': 32}
  • id: 144308268
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 15, 'group_counter': 47489, 'group_order': 1728, 'label': '3G-1', 'order': 3, 'powers': [14, 1], 'representative': 134709201, 'size': 32}
  • id: 144308269
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 16, 'group_counter': 47489, 'group_order': 1728, 'label': '3H1', 'order': 3, 'powers': [17, 1], 'representative': 168018561, 'size': 32}
  • id: 144308270
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 17, 'group_counter': 47489, 'group_order': 1728, 'label': '3H-1', 'order': 3, 'powers': [16, 1], 'representative': 134709224, 'size': 32}
  • id: 144308271
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 18, 'group_counter': 47489, 'group_order': 1728, 'label': '3I1', 'order': 3, 'powers': [19, 1], 'representative': 168018938, 'size': 32}
  • id: 144308272
    {'aut_label': '3G1', 'centralizer': '32.a1.a1', 'counter': 19, 'group_counter': 47489, 'group_order': 1728, 'label': '3I-1', 'order': 3, 'powers': [18, 1], 'representative': 134709445, 'size': 32}
  • id: 144308274
    {'aut_label': '4A', 'centralizer': '6.e1.a1', 'counter': 20, 'group_counter': 47489, 'group_order': 1728, 'label': '4A', 'order': 4, 'powers': [2, 20], 'representative': 25880682240, 'size': 6}
  • id: 144308275
    {'aut_label': '4A', 'centralizer': '6.e1.b1', 'counter': 21, 'group_counter': 47489, 'group_order': 1728, 'label': '4B', 'order': 4, 'powers': [2, 21], 'representative': 25877058480, 'size': 6}
  • id: 144308276
    {'aut_label': '4C', 'centralizer': '36.k1.a1', 'counter': 22, 'group_counter': 47489, 'group_order': 1728, 'label': '4C', 'order': 4, 'powers': [3, 22], 'representative': 14959292, 'size': 36}
  • id: 144308277
    {'aut_label': '4C', 'centralizer': '36.k1.a1', 'counter': 23, 'group_counter': 47489, 'group_order': 1728, 'label': '4D', 'order': 4, 'powers': [3, 23], 'representative': 6346776812, 'size': 36}
  • id: 144308278
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 47489, 'group_order': 1728, 'label': '6A1', 'order': 6, 'powers': [7, 2], 'representative': 6314117498, 'size': 1}
  • id: 144308279
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 47489, 'group_order': 1728, 'label': '6A-1', 'order': 6, 'powers': [6, 2], 'representative': 6314117365, 'size': 1}
  • id: 144308280
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 47489, 'group_order': 1728, 'label': '6B', 'order': 6, 'powers': [8, 2], 'representative': 6314117475, 'size': 2}
  • id: 144308281
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 47489, 'group_order': 1728, 'label': '6C1', 'order': 6, 'powers': [10, 2], 'representative': 6314117144, 'size': 2}
  • id: 144308282
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 47489, 'group_order': 1728, 'label': '6C-1', 'order': 6, 'powers': [9, 2], 'representative': 6314117121, 'size': 2}
  • id: 144308283
    {'aut_label': '6D1', 'centralizer': '6.f1.a1', 'counter': 29, 'group_counter': 47489, 'group_order': 1728, 'label': '6D1', 'order': 6, 'powers': [6, 3], 'representative': 7625845, 'size': 6}
  • id: 144308285
    {'aut_label': '6D1', 'centralizer': '6.f1.a1', 'counter': 30, 'group_counter': 47489, 'group_order': 1728, 'label': '6D-1', 'order': 6, 'powers': [7, 3], 'representative': 7625978, 'size': 6}
  • id: 144308286
    {'aut_label': '6E', 'centralizer': '12.g1.a1', 'counter': 31, 'group_counter': 47489, 'group_order': 1728, 'label': '6E', 'order': 6, 'powers': [8, 3], 'representative': 7625868, 'size': 12}
  • id: 144308287
    {'aut_label': '6F1', 'centralizer': '12.g1.a1', 'counter': 32, 'group_counter': 47489, 'group_order': 1728, 'label': '6F1', 'order': 6, 'powers': [9, 3], 'representative': 7625601, 'size': 12}
  • id: 144308288
    {'aut_label': '6F1', 'centralizer': '12.g1.a1', 'counter': 33, 'group_counter': 47489, 'group_order': 1728, 'label': '6F-1', 'order': 6, 'powers': [10, 3], 'representative': 7625624, 'size': 12}
  • id: 144308289
    {'aut_label': '6G1', 'centralizer': '12.c1.a1', 'counter': 34, 'group_counter': 47489, 'group_order': 1728, 'label': '6G1', 'order': 6, 'powers': [9, 4], 'representative': 13902013521, 'size': 12}
  • id: 144308290
    {'aut_label': '6G1', 'centralizer': '12.c1.a1', 'counter': 35, 'group_counter': 47489, 'group_order': 1728, 'label': '6G-1', 'order': 6, 'powers': [10, 4], 'representative': 13902013544, 'size': 12}
  • id: 144308291
    {'aut_label': '6G1', 'centralizer': '12.c1.a1', 'counter': 36, 'group_counter': 47489, 'group_order': 1728, 'label': '6H1', 'order': 6, 'powers': [9, 4], 'representative': 13902013710, 'size': 12}
  • id: 144308292
    {'aut_label': '6G1', 'centralizer': '12.c1.a1', 'counter': 37, 'group_counter': 47489, 'group_order': 1728, 'label': '6H-1', 'order': 6, 'powers': [10, 4], 'representative': 13902013824, 'size': 12}
  • id: 144308293
    {'aut_label': '6I1', 'centralizer': '12.c1.a1', 'counter': 38, 'group_counter': 47489, 'group_order': 1728, 'label': '6I1', 'order': 6, 'powers': [6, 4], 'representative': 13902013765, 'size': 12}
  • id: 144308294
    {'aut_label': '6I1', 'centralizer': '12.c1.a1', 'counter': 39, 'group_counter': 47489, 'group_order': 1728, 'label': '6I-1', 'order': 6, 'powers': [7, 4], 'representative': 13902013898, 'size': 12}
  • id: 144308296
    {'aut_label': '6J1', 'centralizer': '12.c1.a1', 'counter': 40, 'group_counter': 47489, 'group_order': 1728, 'label': '6J1', 'order': 6, 'powers': [8, 4], 'representative': 13902013788, 'size': 12}
  • id: 144308297
    {'aut_label': '6J1', 'centralizer': '12.c1.a1', 'counter': 41, 'group_counter': 47489, 'group_order': 1728, 'label': '6J-1', 'order': 6, 'powers': [8, 4], 'representative': 13902013875, 'size': 12}
  • id: 144308298
    {'aut_label': '6K', 'centralizer': '32.a1.a1', 'counter': 42, 'group_counter': 47489, 'group_order': 1728, 'label': '6K', 'order': 6, 'powers': [11, 2], 'representative': 6278635440, 'size': 32}
  • id: 144308299
    {'aut_label': '6K', 'centralizer': '32.a1.a1', 'counter': 43, 'group_counter': 47489, 'group_order': 1728, 'label': '6L', 'order': 6, 'powers': [12, 2], 'representative': 6278635788, 'size': 32}
  • id: 144308300
    {'aut_label': '6K', 'centralizer': '32.a1.a1', 'counter': 44, 'group_counter': 47489, 'group_order': 1728, 'label': '6M', 'order': 6, 'powers': [13, 2], 'representative': 6278635875, 'size': 32}
  • id: 144308301
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 45, 'group_counter': 47489, 'group_order': 1728, 'label': '6N1', 'order': 6, 'powers': [14, 2], 'representative': 6278635521, 'size': 32}
  • id: 144308302
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 46, 'group_counter': 47489, 'group_order': 1728, 'label': '6N-1', 'order': 6, 'powers': [15, 2], 'representative': 6278635824, 'size': 32}
  • id: 144308303
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 47, 'group_counter': 47489, 'group_order': 1728, 'label': '6O1', 'order': 6, 'powers': [16, 2], 'representative': 6278635544, 'size': 32}
  • id: 144308304
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 48, 'group_counter': 47489, 'group_order': 1728, 'label': '6O-1', 'order': 6, 'powers': [17, 2], 'representative': 6278635710, 'size': 32}
  • id: 144308305
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 49, 'group_counter': 47489, 'group_order': 1728, 'label': '6P1', 'order': 6, 'powers': [18, 2], 'representative': 6278635765, 'size': 32}
  • id: 144308307
    {'aut_label': '6N1', 'centralizer': '32.a1.a1', 'counter': 50, 'group_counter': 47489, 'group_order': 1728, 'label': '6P-1', 'order': 6, 'powers': [19, 2], 'representative': 6278635898, 'size': 32}
  • id: 144308308
    {'aut_label': '6Q1', 'centralizer': '72.k1.a1', 'counter': 51, 'group_counter': 47489, 'group_order': 1728, 'label': '6Q1', 'order': 6, 'powers': [6, 5], 'representative': 13898304604, 'size': 72}
  • id: 144308309
    {'aut_label': '6Q1', 'centralizer': '72.k1.a1', 'counter': 52, 'group_counter': 47489, 'group_order': 1728, 'label': '6Q-1', 'order': 6, 'powers': [7, 5], 'representative': 13898304161, 'size': 72}
  • id: 144308310
    {'aut_label': '8A', 'centralizer': '72.bh1.a1', 'counter': 53, 'group_counter': 47489, 'group_order': 1728, 'label': '8A', 'order': 8, 'powers': [20, 53], 'representative': 40279720456, 'size': 72}
  • id: 144308311
    {'aut_label': '8A', 'centralizer': '72.bh1.b1', 'counter': 54, 'group_counter': 47489, 'group_order': 1728, 'label': '8B', 'order': 8, 'powers': [21, 54], 'representative': 20611664776, 'size': 72}
  • id: 144308312
    {'aut_label': '12A1', 'centralizer': '6.e1.a1', 'counter': 55, 'group_counter': 47489, 'group_order': 1728, 'label': '12A1', 'order': 12, 'powers': [24, 20], 'representative': 32732870005, 'size': 6}
  • id: 144308313
    {'aut_label': '12A1', 'centralizer': '6.e1.a1', 'counter': 56, 'group_counter': 47489, 'group_order': 1728, 'label': '12A-1', 'order': 12, 'powers': [25, 20], 'representative': 20801370698, 'size': 6}
  • id: 144308314
    {'aut_label': '12A1', 'centralizer': '6.e1.b1', 'counter': 57, 'group_counter': 47489, 'group_order': 1728, 'label': '12B1', 'order': 12, 'powers': [25, 21], 'representative': 40443787898, 'size': 6}
  • id: 144308315
    {'aut_label': '12A1', 'centralizer': '6.e1.b1', 'counter': 58, 'group_counter': 47489, 'group_order': 1728, 'label': '12B-1', 'order': 12, 'powers': [24, 21], 'representative': 46594961605, 'size': 6}
  • id: 144308316
    {'aut_label': '12C', 'centralizer': '12.b1.a1', 'counter': 59, 'group_counter': 47489, 'group_order': 1728, 'label': '12C', 'order': 12, 'powers': [26, 20], 'representative': 13941935628, 'size': 12}
  • id: 144308318
    {'aut_label': '12C', 'centralizer': '12.b1.b1', 'counter': 60, 'group_counter': 47489, 'group_order': 1728, 'label': '12D', 'order': 12, 'powers': [26, 21], 'representative': 13945559388, 'size': 12}
  • id: 144308319
    {'aut_label': '12E1', 'centralizer': '12.b1.a1', 'counter': 61, 'group_counter': 47489, 'group_order': 1728, 'label': '12E1', 'order': 12, 'powers': [27, 20], 'representative': 13941935361, 'size': 12}
  • id: 144308320
    {'aut_label': '12E1', 'centralizer': '12.b1.a1', 'counter': 62, 'group_counter': 47489, 'group_order': 1728, 'label': '12E-1', 'order': 12, 'powers': [28, 20], 'representative': 13941935384, 'size': 12}
  • id: 144308321
    {'aut_label': '12E1', 'centralizer': '12.b1.b1', 'counter': 63, 'group_counter': 47489, 'group_order': 1728, 'label': '12F1', 'order': 12, 'powers': [27, 21], 'representative': 13945559121, 'size': 12}
  • id: 144308322
    {'aut_label': '12E1', 'centralizer': '12.b1.b1', 'counter': 64, 'group_counter': 47489, 'group_order': 1728, 'label': '12F-1', 'order': 12, 'powers': [28, 21], 'representative': 13945559144, 'size': 12}
  • id: 144308323
    {'aut_label': '12G1', 'centralizer': '36.k1.a1', 'counter': 65, 'group_counter': 47489, 'group_order': 1728, 'label': '12G1', 'order': 12, 'powers': [29, 22], 'representative': 11335121, 'size': 36}
  • id: 144308324
    {'aut_label': '12G1', 'centralizer': '36.k1.a1', 'counter': 66, 'group_counter': 47489, 'group_order': 1728, 'label': '12G-1', 'order': 12, 'powers': [30, 22], 'representative': 11335144, 'size': 36}
  • id: 144308325
    {'aut_label': '12G1', 'centralizer': '36.k1.a1', 'counter': 67, 'group_counter': 47489, 'group_order': 1728, 'label': '12H1', 'order': 12, 'powers': [29, 23], 'representative': 6270934481, 'size': 36}
  • id: 144308326
    {'aut_label': '12G1', 'centralizer': '36.k1.a1', 'counter': 68, 'group_counter': 47489, 'group_order': 1728, 'label': '12H-1', 'order': 12, 'powers': [30, 23], 'representative': 6270934504, 'size': 36}
  • id: 144308327
    {'aut_label': '24A1', 'centralizer': '72.bh1.a1', 'counter': 69, 'group_counter': 47489, 'group_order': 1728, 'label': '24A1', 'order': 24, 'powers': [55, 53], 'representative': 14026124122, 'size': 72}
  • id: 144308329
    {'aut_label': '24A1', 'centralizer': '72.bh1.a1', 'counter': 70, 'group_counter': 47489, 'group_order': 1728, 'label': '24A-1', 'order': 24, 'powers': [56, 53], 'representative': 46474047189, 'size': 72}
  • id: 144308330
    {'aut_label': '24A1', 'centralizer': '72.bh1.b1', 'counter': 71, 'group_counter': 47489, 'group_order': 1728, 'label': '24B1', 'order': 24, 'powers': [57, 54], 'representative': 26070388389, 'size': 72}
  • id: 144308331
    {'aut_label': '24A1', 'centralizer': '72.bh1.b1', 'counter': 72, 'group_counter': 47489, 'group_order': 1728, 'label': '24B-1', 'order': 24, 'powers': [58, 54], 'representative': 32622998362, 'size': 72}
• 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: 14029548
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.1a', '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], 'schur_index': 1}
  • id: 14029559
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.1b', '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], 'schur_index': 1}
  • id: 14029570
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14029581
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, 2, -2, -2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 1, 1, -2, -2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 14029590
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029591
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029592
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029593
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029552
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, -1, -1, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, -1, 3, 3, -1, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14029553
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, -1, -1, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, 3, 3, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14029554
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, -1, 1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 14029555
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 1, 1, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, -1, -1, 3, 3, -1, 3, -1, -1, 3, 3, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14029556
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, 1, 1, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 3, 3, -1, -1, 3, -1, 3, 3, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14029557
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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: 14029594
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, -2, -2, -2, 1, 1, -2, -2, -2, 4, -2, 1, 1, 1, 1, 4, 4, 0, 0, -2, -2, -2, 1, 1, -2, -2, 1, 1, -2, 1, 1, -2, -2, -2, -2, 1, 1, -2, -2, -2, 4, -2, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029549
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, -2, -2, 1, 1, 4, 4, 0, 0, -2, -2, -2, 1, 1, -2, -2, 1, 1, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, 4, -2, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029550
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, -2, -2, -2, 1, 1, 1, 4, -2, -2, 1, 1, 1, -2, -2, 4, 4, 0, 0, -2, -2, -2, 1, 1, -2, -2, 1, 1, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029551
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.2h', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, -2, -2, 4, -2, -2, 1, -2, -2, -2, 1, 1, 1, 1, 1, 4, 4, 0, 0, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, 4, -2, -2, 1, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029565
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.4a', 'multiplicity': 1, 'nt': [8, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -2, 2, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029566
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.4b', 'multiplicity': 1, 'nt': [8, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, -2, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029558
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3g', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 6, -2, -2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -2, 2, 1, 1, -3, -3, -2, 6, 1, 1, -3, -3, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14029560
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3h', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, -2, -2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -2, -3, -3, 1, 1, 6, -2, -3, -3, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14029561
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3i', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, 6, 6, -2, 2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -3, -3, 6, -3, -3, -3, -3, 1, 1, 1, 1, 1, 1, 6, -2, -2, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 14029562
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3j', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 6, 2, 2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, -2, 1, 1, -3, -3, -2, 6, 1, 1, -3, -3, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14029563
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3k', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, 2, 2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 2, -3, -3, 1, 1, 6, -2, -3, -3, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14029564
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.3l', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, 6, 6, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -3, -3, 6, -3, -3, -3, -3, 1, 1, 1, 1, 1, 1, 6, -2, -2, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14029569
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, -2, 2, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 6, 6, 6, 6, 6, -2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029571
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6b', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 6, 6, -3, -3, -3, -2, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 6, 6, 1, -3, 1, 1, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029572
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6c', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 6, 6, -3, -3, -3, -2, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -2, -2, -3, 1, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029573
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6d', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, 6, 6, -2, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 6, 6, -3, -3, -3, 6, 6, 1, 1, -2, 1, 1, -2, -3, 1, 1, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029567
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.4c', 'multiplicity': 2, 'nt': [24, 1406], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, -4, -4, 8, -4, -4, -1, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, -4, 4, 4, 4, -8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029568
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.4d', 'multiplicity': 2, 'nt': [24, 1406], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, -4, -4, 8, -4, -4, -1, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 4, -4, 4, 4, -8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029582
    {'cdim': 8, 'counter': 40, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8a', 'multiplicity': 1, 'nt': [24, 332], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 14029583
    {'cdim': 8, 'counter': 41, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8b', 'multiplicity': 1, 'nt': [24, 1404], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 8, 8, -4, -4, -4, -1, -1, 2, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, -8, -8, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, -2, -2, 1, 1, 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: 14029584
    {'cdim': 8, 'counter': 42, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8c', 'multiplicity': 1, 'nt': [24, 1404], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 8, 8, -4, -4, -4, -1, 2, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, -8, -8, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, 1, 1, -2, -2, 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: 14029585
    {'cdim': 8, 'counter': 43, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8d', 'multiplicity': 1, 'nt': [24, 1404], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 8, 8, -4, -4, -4, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -8, -8, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 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: 14029574
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6e', 'multiplicity': 2, 'nt': [24, 564], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 12, 0, 0, -6, -6, -6, 3, 3, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, -6, 2, -6, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029575
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6f', 'multiplicity': 2, 'nt': [24, 564], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -4, 0, 0, -6, -6, -6, 3, 3, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 2, 2, -6, 2, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029576
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6g', 'multiplicity': 2, 'nt': [24, 564], 'qdim': 12, 'qvalues': [12, 12, 12, -4, 0, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -6, -6, -6, 3, 3, -6, -6, -1, -1, 2, -1, -1, 2, -6, 2, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029577
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6h', 'multiplicity': 2, 'nt': [24, 699], 'qdim': 12, 'qvalues': [12, 12, -4, 4, 0, 12, 12, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 12, 12, -6, -6, -6, -4, -4, -2, -2, 4, -2, -2, 4, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029578
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6i', 'multiplicity': 2, 'nt': [24, 700], 'qdim': 12, 'qvalues': [12, 12, -4, 4, 0, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -6, -6, 12, -6, -6, 2, 2, -2, -2, -2, -2, -2, -2, -4, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029579
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6j', 'multiplicity': 2, 'nt': [24, 2653], 'qdim': 12, 'qvalues': [12, 12, -4, 4, 0, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -6, -6, -6, 3, 3, 2, 2, -5, -5, -2, 7, 7, -2, 2, -2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029580
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.6k', 'multiplicity': 2, 'nt': [24, 2653], 'qdim': 12, 'qvalues': [12, 12, -4, 4, 0, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -6, -6, -6, 3, 3, 2, 2, 7, 7, -2, -5, -5, -2, 2, -2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14029586
    {'cdim': 8, 'counter': 44, 'faithful': True, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8e', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, -8, 4, 4, -2, -2, -2, 4, -2, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, 2, -1, -1, -1, -1, 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: 14029587
    {'cdim': 8, 'counter': 45, 'faithful': True, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8f', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, -8, 4, 4, 1, -2, 4, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 8, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, 2, 2, -1, 2, 2, -1, -1, 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: 14029588
    {'cdim': 8, 'counter': 46, 'faithful': True, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8g', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, -8, 4, 4, 1, 4, -2, -2, 1, 1, 1, -2, -2, 0, 0, 0, 0, 8, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -4, 2, -1, -1, -1, 2, 2, 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: 14029589
    {'cdim': 8, 'counter': 47, 'faithful': False, 'group': '1728.47489', 'group_order': 1728, 'image': None, 'label': '1728.47489.8h', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, 16, -8, -8, 1, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8, -16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, -1, -1, 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}
• 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: 33333713
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1728, 'label': '1728.47489.1a', '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]]]}
  • id: 33333724
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 864, 'label': '1728.47489.1b', '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]]]}
  • id: 33333735
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 576, 'label': '1728.47489.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33333746
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 576, 'label': '1728.47489.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33333757
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 288, 'label': '1728.47489.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33333768
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 288, 'label': '1728.47489.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33333779
    {'center': '6.b1.c1', 'center_index': 6, 'center_order': 288, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.c1', 'kernel_order': 288, 'label': '1728.47489.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333783
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 288, 'label': '1728.47489.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333784
    {'center': '6.b1.b1', 'center_index': 6, 'center_order': 288, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.b1', 'kernel_order': 288, 'label': '1728.47489.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333714
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 288, 'label': '1728.47489.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333715
    {'center': '6.b1.b1', 'center_index': 6, 'center_order': 288, 'counter': 11, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 96, 'label': '1728.47489.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333716
    {'center': '6.b1.b1', 'center_index': 6, 'center_order': 288, 'counter': 12, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 96, 'label': '1728.47489.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333717
    {'center': '6.b1.c1', 'center_index': 6, 'center_order': 288, 'counter': 13, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.c1', 'kernel_order': 96, 'label': '1728.47489.2f1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333718
    {'center': '6.b1.c1', 'center_index': 6, 'center_order': 288, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.c1', 'kernel_order': 96, 'label': '1728.47489.2f2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333719
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 96, 'label': '1728.47489.2g1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333720
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 96, 'label': '1728.47489.2g2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333721
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 96, 'label': '1728.47489.2h1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 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]]]}
  • id: 33333722
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 96, 'label': '1728.47489.2h2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 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]]]}
  • id: 33333723
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.b1', 'kernel_order': 72, 'label': '1728.47489.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33333725
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 72, 'label': '1728.47489.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 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]]]}
  • id: 33333726
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 72, 'label': '1728.47489.3c', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 33333727
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.b1', 'kernel_order': 72, 'label': '1728.47489.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33333728
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 72, 'label': '1728.47489.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 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]]]}
  • id: 33333729
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 72, 'label': '1728.47489.3f', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 33333730
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 25, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.b1', 'kernel_order': 24, 'label': '1728.47489.3g1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[3, -1]], [[3, 1]], [[-1, 0]], [[3, 0]], [[-1, -1]], [[-1, 1]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33333731
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 26, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.b1', 'kernel_order': 24, 'label': '1728.47489.3g2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[3, 1]], [[3, -1]], [[-1, 0]], [[3, 0]], [[-1, 1]], [[-1, -1]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33333732
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 27, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.a1', 'kernel_order': 24, 'label': '1728.47489.3h1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33333733
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 28, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.a1', 'kernel_order': 24, 'label': '1728.47489.3h2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33333734
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 29, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.47489.3i1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33333736
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 30, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.47489.3i2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33333737
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.b1', 'kernel_order': 24, 'label': '1728.47489.3j1', 'nt': [18, 30], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[3, -1]], [[3, 1]], [[-1, 0]], [[3, 0]], [[-1, -1]], [[-1, 1]], [[3, -1]], [[3, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33333738
    {'center': '24.b1.b1', 'center_index': 24, 'center_order': 72, 'counter': 32, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.b1', 'kernel_order': 24, 'label': '1728.47489.3j2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[3, 1]], [[3, -1]], [[-1, 0]], [[3, 0]], [[-1, 1]], [[-1, -1]], [[3, 1]], [[3, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33333739
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 33, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.a1', 'kernel_order': 24, 'label': '1728.47489.3k1', 'nt': [18, 30], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33333740
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 72, 'counter': 34, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.d1.a1', 'kernel_order': 24, 'label': '1728.47489.3k2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33333741
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 35, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.47489.3l1', 'nt': [18, 30], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33333742
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 36, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.47489.3l2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33333743
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '192.1494', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 9, 'label': '1728.47489.4a', 'nt': [8, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333744
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  • id: 33333745
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  • id: 33333747
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  • id: 33333748
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  • id: 33333749
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  • id: 33333750
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  • id: 33333751
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  • id: 33333752
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  • id: 33333753
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  • id: 33333754
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  • id: 33333755
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  • id: 33333756
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  • id: 33333758
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  • id: 33333759
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  • id: 33333760
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 52, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '216.164', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.47489.6g2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 1]], [[-3, -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]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333761
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  • id: 33333762
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 54, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1036', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.47489.6h2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[2, 0]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[2, 0]], [[1, 0]], [[-3, 0], [-4, 1]], [[1, 0], [4, 1]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333763
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 55, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1035', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.47489.6i1', 'nt': [24, 700], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, -1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 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]]]}
  • id: 33333764
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 56, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '288.1035', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.47489.6i2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, -1]], [[6, 1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 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]]]}
  • id: 33333765
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 57, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4709', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.47489.6j1', 'nt': [24, 2653], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-2, 1]], [[-2, -1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[2, 1]], [[4, 0], [1, 1]], [[3, 0], [-1, 1]], [[2, -1]], [[1, 0]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[1, -1]], [[1, 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]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333766
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 58, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4709', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.47489.6j2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-2, -1]], [[-2, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[2, -1]], [[3, 0], [-1, 1]], [[4, 0], [1, 1]], [[2, 1]], [[1, 0]], [[-3, 0], [-4, 1]], [[1, 0], [4, 1]], [[1, 1]], [[1, -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]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333767
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 59, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4709', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.47489.6k1', 'nt': [24, 2653], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-2, 1]], [[-2, -1]], [[3, 0], [-1, 1]], [[4, 0], [1, 1]], [[2, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[2, -1]], [[1, 0]], [[-3, 0], [-4, 1]], [[1, 0], [4, 1]], [[1, -1]], [[1, 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]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333769
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 60, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4709', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.47489.6k2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-2, -1]], [[-2, 1]], [[4, 0], [1, 1]], [[3, 0], [-1, 1]], [[2, -1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[2, 1]], [[1, 0]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[1, 1]], [[1, -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]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333770
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 61, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '192.1494', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 9, 'label': '1728.47489.8a', 'nt': [24, 332], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]]]}
  • id: 33333771
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 62, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8487', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.47489.8b', 'nt': [24, 1404], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[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: 33333772
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 63, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8487', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.47489.8c', 'nt': [24, 1404], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333773
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 64, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8487', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 3, 'label': '1728.47489.8d', 'nt': [24, 1404], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]]]}
  • id: 33333774
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 65, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8e1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, -1]], [[-8, 1]], [[4, 0]], [[4, 1]], [[4, -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]], [[-2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -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]]]}
  • id: 33333775
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8e2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 1]], [[-8, -1]], [[4, 0]], [[4, -1]], [[4, 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]], [[-2, -1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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]]]}
  • id: 33333776
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8f1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, -1]], [[-8, 1]], [[4, 0]], [[4, 1]], [[4, -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]], [[1, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -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]]]}
  • id: 33333777
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8f2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 1]], [[-8, -1]], [[4, 0]], [[4, -1]], [[4, 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]], [[1, -1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 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]]]}
  • id: 33333778
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8g1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, -1]], [[-8, 1]], [[4, 0]], [[4, 1]], [[4, -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]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333780
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '1728.47489', 'image_order': 1728, 'indicator': 0, 'kernel': '1728.a1.a1', 'kernel_order': 1, 'label': '1728.47489.8g2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 1]], [[-8, -1]], [[4, 0]], [[4, -1]], [[4, 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]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33333781
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 71, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8480', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.47489.8h1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[8, 0]], [[8, 1]], [[8, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, -1]], [[-8, 1]], [[-8, 0]], [[-8, 1]], [[-8, -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]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -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]]]}
  • id: 33333782
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 18, 'counter': 72, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.47489', 'group_counter': 47489, 'group_order': 1728, 'image': None, 'image_isoclass': '576.8480', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 3, 'label': '1728.47489.8h2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[8, 0]], [[8, -1]], [[8, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 1]], [[-8, -1]], [[-8, 0]], [[-8, -1]], [[-8, 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]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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]]]}
• 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: 115937765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1728, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1728.47489.1.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': '1728.47489', 'subgroup_hash': 47489, 'subgroup_order': 1728, 'subgroup_tex': '(Q_8\\times C_3^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 864, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.2.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': '864.4609', 'subgroup_hash': 4609, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1728.47489.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8487', 'subgroup_hash': 8487, 'subgroup_order': 576, 'subgroup_tex': '(C_3\\times Q_8):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.3.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': '576.4220', 'subgroup_hash': 4220, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times D_{12}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.3.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': '576.8480', 'subgroup_hash': 8480, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.3.c1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '576.8480', 'subgroup_hash': 8480, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.3.c1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1.c1', 'outer_equivalence': False, 'perfect': False, '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': '576.8480', 'subgroup_hash': 8480, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 115938250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '432.617', 'subgroup_hash': 617, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.4.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.617', 'subgroup_hash': 617, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 288, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1022', 'subgroup_hash': 1022, 'subgroup_order': 288, 'subgroup_tex': 'D_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 288, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 288, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 288, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.c1', '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 288, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.6.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': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.720', 'subgroup_hash': 720, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.720', 'subgroup_hash': 720, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.271', 'subgroup_hash': 271, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '288.271', 'subgroup_hash': 271, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.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': '288.711', 'subgroup_hash': 711, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 115937888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.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': '288.267', 'subgroup_hash': 267, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.6.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.c1', 'outer_equivalence': False, 'perfect': False, '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': '288.987', 'subgroup_hash': 987, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 115937954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 115937965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '216.134', 'subgroup_hash': 134, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.134', 'subgroup_hash': 134, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '192.886', 'subgroup_hash': 886, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '192.800', 'subgroup_hash': 800, 'subgroup_order': 192, 'subgroup_tex': '(C_3\\times D_4):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '192.1494', 'subgroup_hash': 1494, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.9.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '192.1494', 'subgroup_hash': 1494, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.9.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.c1', 'outer_equivalence': False, 'perfect': False, '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': '192.1494', 'subgroup_hash': 1494, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 115938076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.181', 'subgroup_hash': 181, 'subgroup_order': 144, 'subgroup_tex': 'C_4.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.181', 'subgroup_hash': 181, 'subgroup_order': 144, 'subgroup_tex': 'C_4.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.76', 'subgroup_hash': 76, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.75', 'subgroup_hash': 75, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.75', 'subgroup_hash': 75, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 115938176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 115938187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 115938198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '144.80', 'subgroup_hash': 80, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.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': '144.80', 'subgroup_hash': 80, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '144.82', 'subgroup_hash': 82, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.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': '144.82', 'subgroup_hash': 82, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.c1', 'outer_equivalence': False, 'perfect': False, '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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.d1', 'outer_equivalence': False, 'perfect': False, '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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.e1', 'outer_equivalence': False, 'perfect': False, '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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.m1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.f1', 'outer_equivalence': False, 'perfect': False, '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': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 115938222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 96, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 115938225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 96, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 115938226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 96, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.18.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.156', 'subgroup_hash': 156, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '96.156', 'subgroup_hash': 156, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.54', 'subgroup_hash': 54, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.54', 'subgroup_hash': 54, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.44', 'subgroup_hash': 44, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.44', 'subgroup_hash': 44, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.174', 'subgroup_hash': 174, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.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': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.50', 'subgroup_hash': 50, 'subgroup_order': 96, 'subgroup_tex': '\\OD_{16}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.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': '96.40', 'subgroup_hash': 40, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 32, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 115938244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 32, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.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': 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': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.18.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.c1', 'outer_equivalence': False, 'perfect': False, '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': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.24.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': '24.12', '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': 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: 115938248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.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': '72.38', 'subgroup_hash': 38, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', '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': '72.38', 'subgroup_hash': 38, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938260
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.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: 115937774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 115937778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.q1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 115937784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.d1', 'outer_equivalence': False, 'perfect': False, '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: 115937786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.e1', 'outer_equivalence': False, 'perfect': False, '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: 115937787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.r1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.f1', 'outer_equivalence': False, 'perfect': False, '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: 115937789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 115937791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 115937792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 115937793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.c1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.d1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.e1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.u1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.f1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.c1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.d1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.e1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.x1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.f1', 'outer_equivalence': False, 'perfect': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.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: 115937813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.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: 115937814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.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: 115937815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.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: 115937817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.d1', 'outer_equivalence': False, 'perfect': False, '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: 115937819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.e1', 'outer_equivalence': False, 'perfect': False, '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: 115937820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.ba1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.f1', 'outer_equivalence': False, 'perfect': False, '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: 115937822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.24.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1728.47489.27.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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 115937825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.32.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: 115937826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.32.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.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': 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: 115937828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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: 115937829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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: 115937830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115937841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1.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': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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: 115937852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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: 115937858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.t1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115937866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115937867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115937868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.c1', 'outer_equivalence': False, 'perfect': False, '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.d1', 'outer_equivalence': False, 'perfect': False, '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.e1', 'outer_equivalence': False, 'perfect': False, '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.36.y1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.f1', 'outer_equivalence': False, 'perfect': False, '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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 115937875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 115937878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 115937879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 115937880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115937881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 115937883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 115937884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115937885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.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: 115937886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115937887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h2.a1', 'outer_equivalence': False, 'perfect': False, '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: 115937889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 115937891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 115937900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 115937904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.r1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1.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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 115937911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.d1', 'outer_equivalence': False, 'perfect': False, '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: 115937913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.e1', 'outer_equivalence': False, 'perfect': False, '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: 115937914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.48.s1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.f1', 'outer_equivalence': False, 'perfect': False, '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: 115937915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 32, 'counter': 234, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 115937916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.54.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115937923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1728.47489.64.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: 115937924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.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': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', '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: 115937925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.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': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', '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: 115937926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 247, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 115937933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115937935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115937937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.d1', 'outer_equivalence': False, 'perfect': False, '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: 115937939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.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: 115937940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.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: 115937941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.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: 115937942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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: 115937945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115937953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115937957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.t1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 115937962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.x1.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: 115937964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.y1.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: 115937967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.z1.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: 115937969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115937972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 115937973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115937981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115937982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.be1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.c2', 'outer_equivalence': False, 'perfect': False, '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: 115937983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115937984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 115937985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115937986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115937989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 115937990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 115937991
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937992
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bj1.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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115937995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.c1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115937998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.d1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.e1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bk1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.f1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.c1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.d1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.e1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bl1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.f1', 'outer_equivalence': False, 'perfect': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 115938008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bm1.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: 115938011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115938013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 115938015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115938017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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: 115938019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.d1', 'outer_equivalence': False, 'perfect': False, '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: 115938022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.e1', 'outer_equivalence': False, 'perfect': False, '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: 115938023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.72.bq1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.f1', 'outer_equivalence': False, 'perfect': False, '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: 115938024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 18, 'counter': 332, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.96.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': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 115938025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938027
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938031
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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: 115938033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.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: 115938036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.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: 115938039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 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: 115938040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.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': 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: 115938041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.i1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.c2', 'outer_equivalence': False, 'perfect': False, '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: 115938044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.96.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1.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: 115938046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115938048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 115938049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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: 115938050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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: 115938051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 115938052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115938053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115938055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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: 115938056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115938060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.108.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 115938061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938063
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 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: 115938073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938074
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 378, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938075
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 379, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938077
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 380, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938078
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 381, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.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: 115938079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 382, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 383, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.l1.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: 115938081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.p2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.p2.a1', 'outer_equivalence': False, 'perfect': False, '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: 115938086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.q2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q2.a1', 'outer_equivalence': False, 'perfect': False, '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: 115938089
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 391, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 115938090
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 392, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.144.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 115938091
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938092
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 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: 115938093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.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: 115938096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 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: 115938100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.w1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938104
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938105
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938106
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115938107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ba1.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: 115938108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1.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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 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: 115938115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1.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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115938116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.144.bc1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1.c2', 'outer_equivalence': False, 'perfect': False, '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: 115938118
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 9, 'counter': 417, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.192.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': '192.1494', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1494, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'Q_8: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: 115938119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.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: 115938120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.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: 115938124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.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: 115938125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.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: 115938126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 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: 115938127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.192.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 8, 'counter': 426, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.216.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': '216.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], '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: 115938129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 427, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 428, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47489.216.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 115938134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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: 115938135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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: 115938136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 115938141
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 115938142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.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: 115938145
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 441, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938146
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 442, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.216.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 115938147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1.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: 115938149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.216.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 115938151
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 6, 'counter': 447, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.47489.288.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': '288.1036', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1036, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2\\times C_6):S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], '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: 115938152
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 448, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.47489.288.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': '288.1035', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1035, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times C_2^2: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: 115938153
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 2, 'counter': 449, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 450, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 451, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 452, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.d1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 453, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 454, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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: 115938160
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 455, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.e1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 456, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938162
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 457, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938163
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 458, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938164
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 459, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938166
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 460, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938167
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938168
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.k1.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: 115938169
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 463, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.288.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: 115938170
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938171
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938172
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1.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: 115938173
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 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: 115938174
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1.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': 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: 115938175
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938177
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.288.n1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1.c2', 'outer_equivalence': False, 'perfect': False, '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: 115938178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 115938179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938181
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 474, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938182
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 475, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.432.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f2.a1', 'outer_equivalence': False, 'perfect': False, '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: 115938186
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 115938188
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 480, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.432.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938189
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.47489.432.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: 115938191
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 3, 'counter': 483, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1728.47489.576.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': '576.8487', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8487, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_3\\times Q_8):S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938192
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 484, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.47489.576.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': '576.8480', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8480, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times Q_8:S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115938193
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 485, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.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: 115938194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 486, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.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: 115938195
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 487, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 115938196
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 488, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938197
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 489, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.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: 115938199
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 490, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 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: 115938200
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.576.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1.c1', 'outer_equivalence': False, 'perfect': False, '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: 115938201
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 492, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.47489.864.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': '864.4709', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4709, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'D3', 'C6'], '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: 115938202
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 493, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.864.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: 115938203
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.864.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: 115938204
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 495, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.47489.864.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: 115938205
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.47489', 'ambient_counter': 47489, 'ambient_order': 1728, 'ambient_tex': '(Q_8\\times C_3^2):S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 1, 'counter': 496, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1728.47489.1728.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': '1728.47489', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47489, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(Q_8\\times C_3^2):S_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C7'], '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: 115937765
    {'ambient': '1728.47489', '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': '288.a1.a1', 'complements': ['1728.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '3.c1.b1', '3.c1.c1', '4.a1.a1', '4.b1.a1', '4.b1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4754, 2337, 4540, 2819, 6770, 7583, 5689, 2130], 'generators': [87091200, 40367945520, 348, 20801370240, 160796595, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '288.1036', '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': '288.1036'}
  • id: 115937766
    {'ambient': '1728.47489', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1728.46116', 'aut_weyl_index': 8, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.b1', '12.l1.b1', '12.m1.b1', '12.m1.d1', '12.m1.f1', '12.n1.b1', '16.a1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4099, -1, 4175, -1, 6983, -1, 5845, -1], 'generators': [94435139, 348, 160796595, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.4.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '4.b1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 115937767
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.a1.a1'], 'contains': ['48.m1.a1', '72.b1.a1', '72.t1.a1', '72.t1.b1', '72.t1.c1', '96.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4977, -1, 3399, -1, 7520, -1, 1677, -1], 'generators': [87091200, 348, 7625520, 6314117040, 160796618], 'label': '1728.47489.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937768
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.a1.a1'], 'contains': ['48.n1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1', '72.t1.b1', '96.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5156, -1, 4443, -1, 7648, -1, 1743, -1], 'generators': [87091200, 160796160, 7625520, 81, 6314117040], 'label': '1728.47489.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937769
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '8.a1.a1'], 'contains': ['48.n1.b1', '72.r1.a1', '72.s1.b1', '72.t1.b1', '72.t1.c1', '96.e1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5156, -1, 3918, -1, 7648, -1, 2169, -1], 'generators': [87091200, 160796595, 7625520, 81, 6314117040], 'label': '1728.47489.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.k1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937770
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '8.a1.a1'], 'contains': ['48.n1.c1', '72.r1.a1', '72.s1.c1', '72.t1.a1', '72.t1.c1', '96.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5156, -1, 3286, -1, 7648, -1, 1808, -1], 'generators': [87091200, 7625520, 81, 51610035, 6314117040], 'label': '1728.47489.24.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.k1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937771
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.b1.b1', '12.c1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.f1.b1', '72.u1.a1', '72.v1.a1', '72.w1.a1', '72.w1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2916, -1, 7615, -1, 5336, -1, 8209, -1], 'generators': [40367945520, 348, 20797746480, 81, 6314117040], 'label': '1728.47489.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115938168
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.f1.b1', '144.o1.a1', '144.ba1.b1'], 'contains': ['576.c1.a1', '864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2281, -1, 4850, -1, 4747, -1, 6031, -1], 'generators': [81, 40451402880], 'label': '1728.47489.288.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '288.k1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115937772
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '24.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.c1.a1', '12.k1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '72.x1.a1', '72.y1.a1', '72.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3052, -1, 7251, -1, 5054, -1, 8131, -1], 'generators': [348, 20797746480, 81, 6314117040, 13941935280], 'label': '1728.47489.24.m1.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': '24.m1.a1', 'projective_image': '288.1036', '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': '8.3'}
  • id: 115937773
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.k1.b1'], 'contains': ['48.b1.a1', '48.f1.b1', '72.x1.b1', '72.y1.b1', '72.z1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3052, -1, 8216, -1, 5054, -1, 8364, -1], 'generators': [348, 20797746480, 81, 6314117040, 40443787440], 'label': '1728.47489.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.m1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115937774
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1'], 'contains': ['48.b1.a1', '48.o1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '72.bc1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1683, -1, 3174, -1, 8796, -1, 1532, -1], 'generators': [348, 81, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.n1.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': '24.n1.a1', 'projective_image': '288.1036', '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': '12.3'}
  • id: 115937775
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.b1.a1'], 'contains': ['48.p1.a1', '72.ba1.a1', '72.bd1.a1', '72.be1.c1', '72.be1.c2', '96.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [303, -1, 2074, -1, 9098, -1, 1396, -1], 'generators': [458, 160796160, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '288.1036', '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': '12.3'}
  • id: 115937776
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.b1.a1'], 'contains': ['48.p1.b1', '72.ba1.a1', '72.bd1.b1', '72.be1.a1', '72.be1.a2', '96.b1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [303, -1, 1125, -1, 9098, -1, 1294, -1], 'generators': [458, 160796595, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.o1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937777
    {'ambient': '1728.47489', 'aut_centralizer_order': 18, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1089108', 'aut_weyl_index': 18, 'centralizer': '96.a1.a1', 'complements': ['288.n1.b1', '288.n1.b2', '288.n1.c1', '288.n1.c2', '288.n1.a1', '288.n1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.b1.b1', '12.c1.a1', '12.g1.a1', '18.a1.a1', '18.b1.a1', '18.l1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3774, 6512, 7185, 6863, 5058, 4135, 8094, 6618], 'generators': [87091200, 40367945520, 348, 20801370240, 7625520, 81, 6314117040], 'label': '1728.47489.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.b1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115937778
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.b1.a1'], 'contains': ['48.p1.c1', '72.ba1.a1', '72.bd1.c1', '72.be1.b1', '72.be1.b2', '96.b1.c1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [303, -1, 2803, -1, 9098, -1, 1228, -1], 'generators': [458, 51610035, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.o1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937779
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.b1.a1'], 'contains': ['48.q1.a1', '72.bb1.a1', '72.bd1.a1', '72.bd1.b1', '72.bd1.c1', '96.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1110, -1, 2296, -1, 8971, -1, 1462, -1], 'generators': [348, 160796595, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937780
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.b1.a1'], 'contains': ['48.r1.a1', '72.bb1.a1', '72.be1.a1', '72.be1.b1', '72.be1.c1', '96.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [672, -1, 731, -1, 9263, -1, 630, -1], 'generators': [348, 20797746480, 6314117040, 13905647280, 160796618], 'label': '1728.47489.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937781
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.b1.a1'], 'contains': ['48.r1.a2', '72.bb1.a1', '72.be1.a2', '72.be1.b2', '72.be1.c2', '96.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [672, -1, 587, -1, 9263, -1, 714, -1], 'generators': [348, 40364311680, 6314117040, 160796618, 20757824640], 'label': '1728.47489.24.q1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.q1.a2', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937782
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.b1.a1'], 'contains': ['48.s1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.be1.b2', '96.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 1945, -1, 9390, -1, 799, -1], 'generators': [160796160, 81, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937783
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.b1.a1'], 'contains': ['48.s1.b1', '72.bc1.b1', '72.bd1.a1', '72.be1.a2', '72.be1.b1', '96.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 2024, -1, 9390, -1, 864, -1], 'generators': [160796160, 20797746480, 81, 6314117040, 13905647280], 'label': '1728.47489.24.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937784
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '8.b1.a1'], 'contains': ['48.s1.c1', '72.bc1.a1', '72.bd1.b1', '72.be1.b1', '72.be1.c2', '96.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 1763, -1, 9390, -1, 1097, -1], 'generators': [160796595, 81, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937785
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '8.b1.a1'], 'contains': ['48.s1.d1', '72.bc1.b1', '72.bd1.b1', '72.be1.b2', '72.be1.c1', '96.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 1281, -1, 9390, -1, 1163, -1], 'generators': [160796595, 20797746480, 81, 6314117040, 13905647280], 'label': '1728.47489.24.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937786
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '8.b1.a1'], 'contains': ['48.s1.e1', '72.bc1.a1', '72.bd1.c1', '72.be1.a2', '72.be1.c1', '96.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 665, -1, 9390, -1, 995, -1], 'generators': [81, 51610035, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.24.r1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.e1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.e1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937787
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '8.b1.a1'], 'contains': ['48.s1.f1', '72.bc1.b1', '72.bd1.c1', '72.be1.a1', '72.be1.c2', '96.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [464, -1, 481, -1, 9390, -1, 929, -1], 'generators': [20797746480, 81, 51610035, 6314117040, 13905647280], 'label': '1728.47489.24.r1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.r1.f1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937805
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.c1.b1'], 'contains': ['72.bj1.b1', '72.bk1.b1', '72.bl1.b1', '72.bl1.d1', '96.e1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 2957, -1, 8550, -1, 2605, -1], 'generators': [160796160, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '24.x1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937788
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': ['288.m1.a1', '288.n1.c1', '288.n1.c2', '288.n1.b1', '288.n1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['18.a1.a1', '18.c1.a1', '18.m1.c1', '24.h1.a1', '24.o1.a1', '24.u1.a1', '24.u1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2344, 3766, 4338, 2209, 7574, 6481, 3335, 3598], 'generators': [87091200, 458, 40367945520, 20801370240, 160796160, 7625520, 6314117040], 'label': '1728.47489.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '288.1036', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115937789
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '72.bf1.a1', '72.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6391, -1, 7190, -1, 2786, -1, 7893, -1], 'generators': [90801299, 348, 81, 6314117040, 13941935280], 'label': '1728.47489.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.s1.a1', 'projective_image': '288.1036', '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': '24.8'}
  • id: 115937790
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.k1.b1', '12.l1.b1'], 'contains': ['48.c1.a1', '48.f1.b1', '72.bf1.b1', '72.bg1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6391, -1, 8303, -1, 2786, -1, 8518, -1], 'generators': [90801299, 348, 81, 13945559040, 6314117040], 'label': '1728.47489.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.s1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 115937791
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.f1.a1', '72.bh1.a1', '72.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4347, -1, 7316, -1, 3901, -1, 7973, -1], 'generators': [348, 40440078659, 81, 6314117040, 13941935280], 'label': '1728.47489.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.t1.a1', 'projective_image': '288.1036', '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': '24.14'}
  • id: 115937792
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.k1.b1', '12.l1.b1'], 'contains': ['48.f1.b1', '72.bh1.b1', '72.bi1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4347, -1, 8650, -1, 3901, -1, 8599, -1], 'generators': [40356979139, 348, 81, 13945559040, 6314117040], 'label': '1728.47489.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.t1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115937793
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.c1.a1', '12.m1.a1'], 'contains': ['72.c1.a1', '72.bk1.a1', '72.bl1.e1', '96.b1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 2710, -1, 8081, -1, 3298, -1], 'generators': [458, 40367945520, 20801370240, 160796160, 6314117040], 'label': '1728.47489.24.u1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.u1.a1', 'projective_image': '288.1036', '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': '24.12'}
  • id: 115937794
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.c1.b1', '12.m1.b1'], 'contains': ['72.c1.b1', '72.bk1.b1', '72.bl1.f1', '96.b1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 4364, -1, 8081, -1, 4299, -1], 'generators': [458, 160796160, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.u1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '24.u1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937795
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.c1.a1', '12.m1.c1'], 'contains': ['72.c1.a1', '72.bk1.c1', '72.bl1.a1', '96.b1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 1374, -1, 8081, -1, 4818, -1], 'generators': [458, 40367945520, 20801370240, 160796595, 6314117040], 'label': '1728.47489.24.u1.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.u1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937796
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.c1.b1', '12.m1.d1'], 'contains': ['72.c1.b1', '72.bk1.d1', '72.bl1.b1', '96.b1.b1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 3591, -1, 8081, -1, 4938, -1], 'generators': [458, 160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.u1.d1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '24.u1.d1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937797
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.c1.a1', '12.m1.e1'], 'contains': ['72.c1.a1', '72.bk1.e1', '72.bl1.c1', '96.b1.c1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 3091, -1, 8081, -1, 3197, -1], 'generators': [458, 40367945520, 20801370240, 51610035, 6314117040], 'label': '1728.47489.24.u1.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.u1.e1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937798
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.c1.b1', '12.m1.f1'], 'contains': ['72.c1.b1', '72.bk1.f1', '72.bl1.d1', '96.b1.c1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1836, -1, 4258, -1, 8081, -1, 4198, -1], 'generators': [458, 51610035, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.u1.f1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '24.u1.f1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937799
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': ['288.m1.a1', '288.n1.c1', '288.n1.c2', '288.n1.a1', '288.n1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.b1'], 'contains': ['18.a1.a1', '18.c1.b1', '18.m1.a1', '24.h1.b1', '24.o1.b1', '24.u1.c1', '24.u1.d1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2344, 3766, 3024, 3730, 7574, 6481, 4689, 2130], 'generators': [87091200, 458, 40367945520, 20801370240, 160796595, 7625520, 6314117040], 'label': '1728.47489.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '288.1036', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115937800
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.c1.a1', '12.n1.a1'], 'contains': ['72.d1.a1', '72.bk1.a1', '72.bk1.c1', '72.bk1.e1', '96.c1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2118, -1, 2617, -1, 7811, -1, 4419, -1], 'generators': [40367945520, 348, 20801370240, 160796595, 6314117040], 'label': '1728.47489.24.v1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.v1.a1', 'projective_image': '864.4709', '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': '24.12'}
  • id: 115937801
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.c1.b1', '12.n1.b1'], 'contains': ['72.d1.b1', '72.bk1.b1', '72.bk1.d1', '72.bk1.f1', '96.c1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2118, -1, 3985, -1, 7811, -1, 4651, -1], 'generators': [348, 160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.v1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '24.v1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937802
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.c1.a1'], 'contains': ['72.d1.a1', '72.bl1.a1', '72.bl1.c1', '72.bl1.e1', '96.d1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1528, -1, 155, -1, 8315, -1, 1929, -1], 'generators': [40367945520, 348, 20801370240, 6314117040, 160796618], 'label': '1728.47489.24.w1.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': '24.w1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937803
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.c1.b1'], 'contains': ['72.d1.b1', '72.bl1.b1', '72.bl1.d1', '72.bl1.f1', '96.d1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1528, -1, 1586, -1, 8315, -1, 2271, -1], 'generators': [348, 13945559040, 6314117040, 160796618, 40443787440], 'label': '1728.47489.24.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '24.w1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937804
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.c1.a1'], 'contains': ['72.bj1.a1', '72.bk1.a1', '72.bl1.a1', '72.bl1.c1', '96.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 1021, -1, 8550, -1, 2086, -1], 'generators': [40367945520, 20801370240, 160796160, 81, 6314117040], 'label': '1728.47489.24.x1.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': '24.x1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937806
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '8.c1.a1'], 'contains': ['72.bj1.a1', '72.bk1.c1', '72.bl1.c1', '72.bl1.e1', '96.e1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 809, -1, 8550, -1, 2707, -1], 'generators': [40367945520, 20801370240, 160796595, 81, 6314117040], 'label': '1728.47489.24.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '24.x1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937807
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '8.c1.b1'], 'contains': ['72.bj1.b1', '72.bk1.d1', '72.bl1.d1', '72.bl1.f1', '96.e1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 2539, -1, 8550, -1, 2909, -1], 'generators': [160796595, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.x1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '24.x1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937808
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '8.c1.a1'], 'contains': ['72.bj1.a1', '72.bk1.e1', '72.bl1.a1', '72.bl1.e1', '96.e1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 77, -1, 8550, -1, 2428, -1], 'generators': [40367945520, 20801370240, 81, 51610035, 6314117040], 'label': '1728.47489.24.x1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '24.x1.e1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.e1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937809
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '8.c1.b1'], 'contains': ['72.bj1.b1', '72.bk1.f1', '72.bl1.b1', '72.bl1.f1', '96.e1.c1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1351, -1, 1509, -1, 8550, -1, 2808, -1], 'generators': [81, 51610035, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.x1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '24.x1.f1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937810
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': ['288.m1.a1', '288.n1.b1', '288.n1.b2', '288.n1.a1', '288.n1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.c1'], 'contains': ['18.a1.a1', '18.c1.c1', '18.m1.b1', '24.h1.c1', '24.o1.c1', '24.u1.e1', '24.u1.f1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2344, 3766, 3961, 5253, 7574, 6481, 3245, 5065], 'generators': [87091200, 458, 40367945520, 20801370240, 7625520, 51610035, 6314117040], 'label': '1728.47489.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '288.1036', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115937811
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.i1.a1', '72.bm1.a1', '72.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8983, -1, 9793, -1, 342, -1, 9883, -1], 'generators': [348, 7625520, 81, 11335619, 13905647280], 'label': '1728.47489.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '576.8487', '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: 115937812
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.i1.b1', '72.bm1.b1', '72.bn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8983, -1, 9873, -1, 342, -1, 9964, -1], 'generators': [6321450899, 348, 7625520, 81, 13905647280], 'label': '1728.47489.24.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.y1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115937813
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.h1.a1'], 'contains': ['48.h2.a1', '48.i1.a1', '48.j1.a1', '72.bo1.a1', '72.bp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9367, -1, 8504, -1, 1499, -1, 5462, -1], 'generators': [87091200, 348, 7625520, 81, 11335619], 'label': '1728.47489.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.z1.a1', 'projective_image': '576.8487', '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': '12.4'}
  • id: 115937814
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.h1.a1'], 'contains': ['48.h2.a1', '48.i1.b1', '48.j1.a1', '72.bo1.b1', '72.bp1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9367, -1, 8441, -1, 1499, -1, 5381, -1], 'generators': [87091200, 6321450899, 348, 7625520, 81], 'label': '1728.47489.24.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.z1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115937815
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.i1.a1'], 'contains': ['48.k1.a1', '72.bo1.a1', '72.bq1.a1', '96.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 6610, -1, 6440, -1, 3653, -1], 'generators': [87091200, 458, 160796160, 7625520, 11335619], 'label': '1728.47489.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '24.ba1.a1', 'projective_image': '576.8487', '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': '24.12'}
  • id: 115937816
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.i1.a1'], 'contains': ['48.k1.a1', '72.bo1.b1', '72.bq1.b1', '96.i1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 6374, -1, 6440, -1, 3587, -1], 'generators': [87091200, 6321450899, 458, 160796160, 7625520], 'label': '1728.47489.24.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '24.ba1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937817
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.i1.b1'], 'contains': ['48.k1.b1', '72.bo1.a1', '72.bq1.c1', '96.i1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 5957, -1, 6440, -1, 4568, -1], 'generators': [87091200, 458, 160796595, 7625520, 11335619], 'label': '1728.47489.24.ba1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '24.ba1.c1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937818
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.i1.b1'], 'contains': ['48.k1.b1', '72.bo1.b1', '72.bq1.d1', '96.i1.b2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 5865, -1, 6440, -1, 4502, -1], 'generators': [87091200, 6321450899, 458, 160796595, 7625520], 'label': '1728.47489.24.ba1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '24.ba1.d1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937819
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.i1.c1'], 'contains': ['48.k1.c1', '72.bo1.a1', '72.bq1.e1', '96.i1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 6487, -1, 6440, -1, 3503, -1], 'generators': [87091200, 458, 7625520, 51610035, 11335619], 'label': '1728.47489.24.ba1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '24.ba1.e1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937820
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.i1.c1'], 'contains': ['48.k1.c1', '72.bo1.b1', '72.bq1.f1', '96.i1.c2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5738, -1, 6256, -1, 6440, -1, 3419, -1], 'generators': [87091200, 6321450899, 458, 7625520, 51610035], 'label': '1728.47489.24.ba1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '24.ba1.f1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937821
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.155790', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': ['288.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.c1.b1', '18.c1.c1', '24.i1.a1', '24.p1.a1', '24.v1.a1', '24.v1.b1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2502, 1172, 3864, 688, 7362, 8696, 4348, 663], 'generators': [87091200, 40367945520, 348, 20801370240, 160796595, 7625520, 6314117040], 'label': '1728.47489.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['18.b1.a1', '18.c1.a1', '18.c1.c1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '864.4709', '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': '96.227'}
  • id: 115937822
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '432.523', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.j1.a1'], 'contains': ['48.l1.a1', '72.bp1.a1', '72.bq1.a1', '72.bq1.c1', '72.bq1.e1', '96.j1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5979, -1, 6321, -1, 6296, -1, 3836, -1], 'generators': [87091200, 348, 160796595, 7625520, 11335619], 'label': '1728.47489.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '1728.47489', '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': '72.43'}
  • id: 115937823
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '432.523', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.j1.a1'], 'contains': ['48.l1.a1', '72.bp1.b1', '72.bq1.b1', '72.bq1.d1', '72.bq1.f1', '96.j1.a2'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5979, -1, 6090, -1, 6296, -1, 3792, -1], 'generators': [87091200, 6321450899, 348, 160796595, 7625520], 'label': '1728.47489.24.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.bb1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 115937824
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 108, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1', '9.c1.b1', '9.c1.c1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.b1.b1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '54.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6131, -1, 6934, -1, 3745, -1, 7248, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '864.4709', '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': '32.27'}
  • id: 115937825
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1', '16.a1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b1.c1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.e1.b1', '96.e1.c1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [990, -1, 2920, -1, 8201, -1, 3020, -1], 'generators': [348, 160796595, 81, 6314117040], 'label': '1728.47489.32.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '288.1036', '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': '2.1'}
  • id: 115937826
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '216.102', 'aut_weyl_index': 64, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.a1.a1'], 'contains': ['64.a1.a1', '96.h1.a1', '96.i1.a1', '96.i1.b1', '96.i1.c1', '96.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4942, -1, 5233, -1, 6661, -1, 4186, -1], 'generators': [90801299, 348, 168018915, 81], 'label': '1728.47489.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '576.8487', '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': '18.4'}
  • id: 115937827
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '216.102', 'aut_weyl_index': 64, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '16.a1.a1'], 'contains': ['64.a1.a1', '96.h1.a1', '96.i1.a2', '96.i1.b2', '96.i1.c2', '96.j1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4942, -1, 4679, -1, 6661, -1, 4105, -1], 'generators': [6241985219, 348, 168018915, 81], 'label': '1728.47489.32.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.b1.a2', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 115937828
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 432, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.h1.a1'], 'contains': ['72.h1.a1', '72.k1.a1', '72.n1.a1', '72.bm1.a1', '72.bm1.b1', '108.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9585, -1, 9147, -1, 843, -1, 9728, -1], 'generators': [458, 7625520, 6314117040, 11335619, 13905647280], 'label': '1728.47489.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '36.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 115937829
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.l1.a1', '72.p1.a1', '72.bn1.a1', '72.bn1.b1', '108.a1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8973, -1, 9639, -1, 700, -1, 9802, -1], 'generators': [348, 7625520, 6314117040, 11335619, 13905647280], 'label': '1728.47489.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.b1.a1', 'projective_image': '864.4709', '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': '24.14'}
  • id: 115937830
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1', '18.d1.a1', '18.f1.a1'], 'contains': ['72.c1.b1', '72.e1.b1', '72.m1.a1', '72.u1.a1', '72.x1.b1', '108.b1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4321, -1, 7369, -1, 4900, -1, 6995, -1], 'generators': [87091200, 458, 40367945520, 20797746480, 6314117040], 'label': '1728.47489.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937831
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.a1.a1', '18.d1.b1', '18.f1.b1'], 'contains': ['72.c1.a1', '72.e1.a1', '72.m1.a1', '72.u1.a1', '72.x1.a1', '108.b1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4321, -1, 7648, -1, 4900, -1, 6737, -1], 'generators': [458, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.c1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937832
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.18491', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.f1.b1', '12.k1.b1', '12.l1.b1', '18.d1.a1', '18.e1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4380, -1, 8115, -1, 3951, -1, 8341, -1], 'generators': [348, 7625520, 20805080339, 81, 6314117040, 20757824640, 13941935280], 'label': '1728.47489.6.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': '288.1036', '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': '96.160'}
  • id: 115937833
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.b1.a1', '18.e1.a1', '18.g1.a1'], 'contains': ['72.d1.b1', '72.f1.b1', '72.o1.a1', '72.v1.a1', '72.y1.b1', '108.b1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3194, -1, 8688, -1, 4742, -1, 8996, -1], 'generators': [87091200, 40367945520, 348, 20797746480, 6314117040], 'label': '1728.47489.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115937834
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.b1.a1', '18.e1.b1', '18.g1.b1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.o1.a1', '72.v1.a1', '72.y1.a1', '108.b1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3194, -1, 7948, -1, 4742, -1, 8849, -1], 'generators': [40367945520, 348, 20801370240, 7625520, 6314117040], 'label': '1728.47489.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937835
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.l1.a1'], 'contains': ['72.g1.c1', '72.g1.d1', '72.q1.a1', '72.w1.a1', '72.w1.b1', '72.z1.b1', '72.bj1.b1', '108.b1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2398, -1, 5544, -1, 6008, -1, 5757, -1], 'generators': [87091200, 40367945520, 20797746480, 81, 6314117040], 'label': '1728.47489.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115937836
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.l1.a1'], 'contains': ['72.g1.a1', '72.g1.b1', '72.q1.a1', '72.w1.a1', '72.w1.b1', '72.z1.a1', '72.bj1.a1', '108.b1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2398, -1, 5418, -1, 6008, -1, 5543, -1], 'generators': [40367945520, 20801370240, 7625520, 81, 6314117040], 'label': '1728.47489.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.e1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 115937837
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1'], 'contains': ['72.e1.a1', '72.e1.b1', '72.h1.a1', '72.u1.a1', '72.x1.a1', '72.x1.b1', '72.ba1.a1', '108.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3723, -1, 5779, -1, 5478, -1, 6810, -1], 'generators': [458, 40367945520, 7625520, 6314117040, 20757824640], 'label': '1728.47489.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '288.1036', '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': '8.5'}
  • id: 115937838
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.b1.a1'], 'contains': ['72.f1.a1', '72.f1.b1', '72.i1.a1', '72.v1.a1', '72.y1.a1', '72.y1.b1', '72.bb1.a1', '108.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2270, -1, 7024, -1, 5194, -1, 8922, -1], 'generators': [40367945520, 348, 7625520, 6314117040, 20757824640], 'label': '1728.47489.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115937839
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.l1.a1'], 'contains': ['72.g1.b1', '72.g1.d1', '72.j1.a1', '72.w1.b1', '72.z1.a1', '72.z1.b1', '72.bc1.b1', '108.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2104, -1, 4053, -1, 6152, -1, 5683, -1], 'generators': [40367945520, 20797746480, 81, 6314117040, 20757824640], 'label': '1728.47489.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115937840
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.l1.a1'], 'contains': ['72.g1.a1', '72.g1.c1', '72.j1.a1', '72.w1.a1', '72.z1.a1', '72.z1.b1', '72.bc1.a1', '108.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2104, -1, 4104, -1, 6152, -1, 5616, -1], 'generators': [40367945520, 7625520, 81, 6314117040, 20757824640], 'label': '1728.47489.36.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.h1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 115937841
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.d1.a1', '18.d1.b1', '18.h1.a1'], 'contains': ['72.k1.a1', '72.m1.a1', '72.bf1.a1', '72.bf1.b1', '108.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7180, -1, 8178, -1, 2173, -1, 7464, -1], 'generators': [90801299, 458, 7625520, 6314117040, 13941935280], 'label': '1728.47489.36.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': '36.i1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115937842
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.e1.a1', '18.e1.b1', '18.i1.a1'], 'contains': ['72.l1.a1', '72.o1.a1', '72.bg1.a1', '72.bg1.b1', '108.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7019, -1, 8422, -1, 2030, -1, 9229, -1], 'generators': [90801299, 348, 7625520, 6314117040, 13941935280], 'label': '1728.47489.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115937843
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.18491', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.b1.b1', '12.d1.a1', '12.f1.a1', '12.k1.a1', '12.l1.a1', '18.d1.b1', '18.e1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4380, -1, 7843, -1, 3951, -1, 8225, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 7625520, 81, 6314117040], 'label': '1728.47489.6.d1.b1', '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.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '96.160'}
  • id: 115937844
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.f1.a1', '18.f1.b1', '18.h1.a1'], 'contains': ['72.m1.a1', '72.n1.a1', '108.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8513, -1, 8304, -1, 1343, -1, 8053, -1], 'generators': [458, 7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.36.k1.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': '36.k1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937845
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.d1.b1', '18.f1.a1', '18.j1.a1'], 'contains': ['72.m1.a1', '72.bh1.a1', '108.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6548, -1, 7498, -1, 3522, -1, 7256, -1], 'generators': [458, 7625520, 20765168579, 6314117040, 13941935280], 'label': '1728.47489.36.l1.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': '36.l1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115937846
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '18.d1.a1', '18.f1.b1', '18.j1.a1'], 'contains': ['72.m1.a1', '72.bh1.b1', '108.f1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6548, -1, 7847, -1, 3522, -1, 7680, -1], 'generators': [458, 7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.36.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.l1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937847
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.g1.a1', '18.g1.b1', '18.i1.a1'], 'contains': ['72.o1.a1', '72.p1.a1', '108.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8299, -1, 9231, -1, 1187, -1, 9574, -1], 'generators': [348, 7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '864.4709', '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: 115937848
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.e1.b1', '18.g1.a1', '18.k1.a1'], 'contains': ['72.o1.a1', '72.bi1.a1', '108.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6219, -1, 8808, -1, 2625, -1, 9146, -1], 'generators': [348, 7625520, 20765168579, 6314117040, 13941935280], 'label': '1728.47489.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.n1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115937849
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '18.e1.a1', '18.g1.b1', '18.k1.a1'], 'contains': ['72.o1.a1', '72.bi1.b1', '108.f1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6219, -1, 8946, -1, 2625, -1, 9490, -1], 'generators': [348, 7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.36.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.n1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115937850
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.a1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.e1.b1', '72.h1.a1', '72.m1.a1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 8062, -1, 3207, -1, 7169, -1], 'generators': [87091200, 458, 40367945520, 7625520, 6314117040], 'label': '1728.47489.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.o1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115937851
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.b1.a1', '18.i1.a1', '18.k1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.f1.b1', '72.i1.a1', '72.o1.a1', '108.g1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7360, -1, 9396, -1, 2929, -1, 9069, -1], 'generators': [87091200, 40367945520, 348, 7625520, 6314117040], 'label': '1728.47489.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.p1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115937852
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.l1.a1'], 'contains': ['72.g1.a1', '72.g1.b1', '72.g1.c1', '72.g1.d1', '72.j1.a1', '72.q1.a1', '72.r1.a1', '108.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6765, -1, 5615, -1, 5714, -1, 5830, -1], 'generators': [87091200, 40367945520, 7625520, 81, 6314117040], 'label': '1728.47489.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.q1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115937853
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 432, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.i1.a1', '12.i1.b1', '12.i1.c1', '18.h1.a1'], 'contains': ['72.a1.a1', '72.k1.a1', '72.n1.a1', '72.bo1.a1', '72.bo1.b1', '108.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9766, -1, 7105, -1, 1800, -1, 5271, -1], 'generators': [87091200, 458, 7625520, 6314117040, 11335619], 'label': '1728.47489.36.r1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '36.r1.a1', 'projective_image': '288.1036', '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': '8.5'}
  • id: 115937854
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 36, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '18.f1.a1', '18.g1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6521, -1, 8260, -1, 2908, -1, 8556, -1], 'generators': [348, 7625520, 81, 6314117040, 11335619, 20757824640, 13941935280], 'label': '1728.47489.6.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': '288.1036', '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': '48.43'}
  • id: 115937855
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.j1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.l1.a1', '72.p1.a1', '72.bp1.a1', '72.bp1.b1', '108.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9209, -1, 9468, -1, 1656, -1, 6184, -1], 'generators': [87091200, 348, 7625520, 6314117040, 11335619], 'label': '1728.47489.36.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.s1.a1', 'projective_image': '864.4709', '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: 115937856
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['72.s1.a1', '72.bq1.a1', '72.bq1.b1', '108.h1.a1', '144.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5751, -1, 6151, -1, 6604, -1, 4012, -1], 'generators': [87091200, 160796160, 7625520, 6314117040, 11335619], 'label': '1728.47489.36.t1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '36.t1.a1', 'projective_image': '864.4709', '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': '24.12'}
  • id: 115937857
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.b1', '12.i1.b1', '12.j1.a1'], 'contains': ['72.s1.b1', '72.bq1.c1', '72.bq1.d1', '108.h1.a1', '144.i1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5751, -1, 5473, -1, 6604, -1, 4734, -1], 'generators': [87091200, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.36.t1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '36.t1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937858
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.c1', '12.i1.c1', '12.j1.a1'], 'contains': ['72.s1.c1', '72.bq1.e1', '72.bq1.f1', '108.h1.a1', '144.i1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5751, -1, 6001, -1, 6604, -1, 3946, -1], 'generators': [87091200, 7625520, 51610035, 6314117040, 11335619], 'label': '1728.47489.36.t1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '36.t1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937859
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.d1.b1'], 'contains': ['72.x1.a1', '72.bf1.a1', '72.bh1.a1', '108.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4675, -1, 6829, -1, 4152, -1, 6922, -1], 'generators': [90801299, 458, 20797746480, 6314117040, 13941935280], 'label': '1728.47489.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.u1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115937860
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '18.d1.a1'], 'contains': ['72.x1.b1', '72.bf1.b1', '72.bh1.b1', '108.i1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4675, -1, 8127, -1, 4152, -1, 7343, -1], 'generators': [90801299, 458, 13945559040, 6314117040, 20757824640], 'label': '1728.47489.36.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.u1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937861
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.e1.b1'], 'contains': ['72.y1.a1', '72.bg1.a1', '72.bi1.a1', '108.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3626, -1, 7600, -1, 3778, -1, 8662, -1], 'generators': [90801299, 348, 20797746480, 6314117040, 13941935280], 'label': '1728.47489.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.v1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115937862
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '18.e1.a1'], 'contains': ['72.y1.b1', '72.bg1.b1', '72.bi1.b1', '108.i1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3626, -1, 8541, -1, 3778, -1, 8786, -1], 'generators': [90801299, 348, 13945559040, 6314117040, 20757824640], 'label': '1728.47489.36.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.v1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115937863
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.m1.a1', '12.m1.c1', '12.m1.e1', '18.d1.b1'], 'contains': ['72.c1.a1', '72.bf1.a1', '72.bh1.a1', '108.j1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4158, -1, 3619, -1, 4409, -1, 6458, -1], 'generators': [90801299, 458, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.36.w1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.w1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115937864
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '12.m1.b1', '12.m1.d1', '12.m1.f1', '18.d1.a1'], 'contains': ['72.c1.b1', '72.bf1.b1', '72.bh1.b1', '108.j1.b1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [4158, -1, 5016, -1, 4409, -1, 6643, -1], 'generators': [458, 94435139, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.36.w1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.w1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937865
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 36, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.b1.b1', '12.e1.a1', '12.f1.b1', '18.f1.b1', '18.g1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6521, -1, 8533, -1, 2908, -1, 8869, -1], 'generators': [40367945520, 348, 20801370240, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.6.e1.b1', '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.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115937866
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.n1.a1', '18.e1.b1'], 'contains': ['72.d1.a1', '72.bg1.a1', '72.bi1.a1', '108.j1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3517, -1, 3869, -1, 4260, -1, 6866, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 6314117040], 'label': '1728.47489.36.x1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.x1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115937867
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '12.n1.b1', '18.e1.a1'], 'contains': ['72.d1.b1', '72.bg1.b1', '72.bi1.b1', '108.j1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3517, -1, 5823, -1, 4260, -1, 7113, -1], 'generators': [94435139, 348, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.36.x1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.x1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115937868
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['72.bk1.a1', '108.j1.a1', '144.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 2763, -1, 7086, -1, 5982, -1], 'generators': [90801299, 40367945520, 20801370240, 6314117040, 168018480], 'label': '1728.47489.36.y1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.a1', 'old_label': '36.y1.a1', 'projective_image': '864.4709', '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': '24.12'}
  • id: 115937869
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '12.m1.b1', '12.n1.b1'], 'contains': ['72.bk1.b1', '108.j1.b1', '144.i1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 4774, -1, 7086, -1, 6086, -1], 'generators': [94435139, 160796160, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.36.y1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.b1', 'old_label': '36.y1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937870
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.b1', '12.m1.c1', '12.n1.a1'], 'contains': ['72.bk1.c1', '108.j1.a1', '144.i1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 2304, -1, 7086, -1, 6246, -1], 'generators': [90801299, 40367945520, 20801370240, 168018915, 6314117040], 'label': '1728.47489.36.y1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.c1', 'old_label': '36.y1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937871
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.b1', '12.m1.d1', '12.n1.b1'], 'contains': ['72.bk1.d1', '108.j1.b1', '144.i1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 4202, -1, 7086, -1, 6307, -1], 'generators': [94435139, 160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.36.y1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.d1', 'old_label': '36.y1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937872
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.c1', '12.m1.e1', '12.n1.a1'], 'contains': ['72.bk1.e1', '108.j1.a1', '144.i1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 3150, -1, 7086, -1, 5940, -1], 'generators': [90801299, 134709555, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.36.y1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.e1', 'old_label': '36.y1.e1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937873
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.c1', '12.m1.f1', '12.n1.b1'], 'contains': ['72.bk1.f1', '108.j1.b1', '144.i1.c1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3344, -1, 4576, -1, 7086, -1, 6025, -1], 'generators': [94435139, 51610035, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.36.y1.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.f1', 'old_label': '36.y1.f1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937874
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '144.a1.a1', '144.b1.a1', '144.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7828, -1, 9319, -1, 2031, -1, 8589, -1], 'generators': [348, 7625520, 81, 6314117040], 'label': '1728.47489.48.a1.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.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937875
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.c1.b1', '24.d1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1', '144.f1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2933, -1, 7811, -1, 4531, -1, 8006, -1], 'generators': [348, 81, 40364311680, 6314117040], 'label': '1728.47489.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115937876
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.jr', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': ['864.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '6.c1.a1', '6.h1.a1', '6.i1.a1', '6.i1.b1', '6.i1.c1', '8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2344, 3127, 3277, 3365, 7574, 6671, 3215, 2860], 'generators': [87091200, 40367945520, 348, 20801370240, 160796595, 7625520, 81, 6314117040], 'label': '1728.47489.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.b1', '6.b1.a1', '6.b1.c1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '288.1036', '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': '96.227'}
  • id: 115937877
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.g1.a1', '12.h1.a1', '18.h1.a1', '18.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8211, -1, 8874, -1, 1926, -1, 8745, -1], 'generators': [87091200, 348, 7625520, 81, 6314117040, 11335619, 13941935280], 'label': '1728.47489.6.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': '288.1036', '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': '48.43'}
  • id: 115937878
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.e1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.a1.a1', '96.h1.a1', '144.g1.a1', '144.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6585, -1, 8306, -1, 2431, -1, 7834, -1], 'generators': [90801299, 348, 81, 6314117040], 'label': '1728.47489.48.c1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.c1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115937879
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.m1.b1', '16.a1.a1'], 'contains': ['96.b1.a1', '96.i1.a1', '96.i1.a2', '144.g1.a1', '144.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4685, -1, 4352, -1, 7289, -1, 4908, -1], 'generators': [90801299, 458, 6314117040, 168018480], 'label': '1728.47489.48.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '48.d1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115937880
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.m1.c1', '12.m1.d1', '16.a1.a1'], 'contains': ['96.b1.b1', '96.i1.b1', '96.i1.b2', '144.g1.a1', '144.i1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4685, -1, 3410, -1, 7289, -1, 5332, -1], 'generators': [90801299, 458, 168018915, 6314117040], 'label': '1728.47489.48.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '48.d1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115937881
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.c1', '12.m1.e1', '12.m1.f1', '16.a1.a1'], 'contains': ['96.b1.c1', '96.i1.c1', '96.i1.c2', '144.g1.a1', '144.i1.c1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4685, -1, 3618, -1, 7289, -1, 4843, -1], 'generators': [90801299, 134709555, 458, 6314117040], 'label': '1728.47489.48.d1.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '48.d1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115937882
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.102', 'aut_weyl_index': 64, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.n1.a1', '12.n1.b1', '16.a1.a1'], 'contains': ['96.c1.a1', '96.j1.a1', '96.j1.a2', '144.h1.a1', '144.i1.a1', '144.i1.b1', '144.i1.c1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4812, -1, 3673, -1, 6854, -1, 5240, -1], 'generators': [90801299, 348, 168018915, 6314117040], 'label': '1728.47489.48.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 115937883
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.f1.a1', '24.l1.a1', '24.m1.a1', '24.s1.a1', '24.t1.a1'], 'contains': ['96.a1.a1', '144.j1.a1', '144.k1.a1', '144.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4142, -1, 7270, -1, 3259, -1, 7946, -1], 'generators': [40367945520, 348, 81, 6314117040], 'label': '1728.47489.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937884
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.c1.b1', '24.f1.a1', '24.l1.a1', '24.m1.b1', '24.s1.b1', '24.t1.b1'], 'contains': ['96.a1.a1', '144.j1.b1', '144.k1.b1', '144.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4142, -1, 8763, -1, 3259, -1, 8065, -1], 'generators': [348, 20761458480, 81, 6314117040], 'label': '1728.47489.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.f1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937885
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.y1.a1', '24.y1.b1'], 'contains': ['96.f1.a1', '96.g1.a1', '144.m1.a1', '144.n1.a1', '144.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7521, -1, 9869, -1, 1953, -1, 9309, -1], 'generators': [87091200, 348, 81, 40364311680], 'label': '1728.47489.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.g1.a1', 'projective_image': '576.8487', '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': '2.1'}
  • id: 115937886
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.y1.a1', '24.y1.b1'], 'contains': ['96.f1.a1', '96.h1.a1', '144.p1.a1', '144.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8107, -1, 9924, -1, 430, -1, 9510, -1], 'generators': [6241985219, 348, 6310483200, 81], 'label': '1728.47489.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '576.8487', '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': '12.4'}
  • id: 115937887
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '48.h2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.z1.a1', '24.z1.b1'], 'contains': ['96.f1.a1', '96.h1.a1', '144.p2.a1', '144.q2.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8221, -1, 8679, -1, 999, -1, 5797, -1], 'generators': [90801299, 348, 7625520, 81], 'label': '1728.47489.48.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.h2.a1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115937888
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1036279', 'aut_weyl_index': 18, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.f1.a1', '12.f1.b1', '12.g1.a1', '18.j1.a1', '18.k1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6945, -1, 8437, -1, 3207, -1, 8437, -1], 'generators': [87091200, 348, 7625520, 20805080339, 81, 6314117040, 13941935280], 'label': '1728.47489.6.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': '288.1036', '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': '96.160'}
  • id: 115937889
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.y1.a1', '24.z1.a1'], 'contains': ['96.f1.a1', '144.r1.a1', '144.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9454, -1, 9724, -1, 158, -1, 9168, -1], 'generators': [348, 7625520, 81, 11335619], 'label': '1728.47489.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.i1.a1', 'projective_image': '576.8487', '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': '12.4'}
  • id: 115937890
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.y1.b1', '24.z1.b1'], 'contains': ['96.f1.a1', '144.r1.b1', '144.s1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9454, -1, 9815, -1, 158, -1, 9436, -1], 'generators': [6321450899, 348, 7625520, 81], 'label': '1728.47489.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.i1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115937891
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.z1.a1', '24.z1.b1'], 'contains': ['96.f1.a1', '144.t1.a1', '144.u1.a1', '144.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8772, -1, 8638, -1, 3056, -1, 5037, -1], 'generators': [87091200, 348, 7625520, 81], 'label': '1728.47489.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '576.8487', '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': '6.1'}
  • id: 115937892
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.h1.a1', '24.ba1.a1', '24.ba1.b1'], 'contains': ['144.t1.a1', '144.w1.a1', '144.x1.c1', '192.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5650, -1, 6478, -1, 7124, -1, 3230, -1], 'generators': [87091200, 458, 160796160, 7625520], 'label': '1728.47489.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '576.8487', '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': '24.12'}
  • id: 115937893
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.h1.b1', '24.ba1.c1', '24.ba1.d1'], 'contains': ['144.t1.a1', '144.w1.b1', '144.x1.a1', '192.b1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5650, -1, 5901, -1, 7124, -1, 4014, -1], 'generators': [87091200, 458, 160796595, 7625520], 'label': '1728.47489.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.k1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937894
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.h1.c1', '24.ba1.e1', '24.ba1.f1'], 'contains': ['144.t1.a1', '144.w1.c1', '144.x1.b1', '192.b1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5650, -1, 6399, -1, 7124, -1, 3128, -1], 'generators': [87091200, 458, 7625520, 51610035], 'label': '1728.47489.48.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.k1.c1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937895
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.i1.a1', '24.bb1.a1', '24.bb1.b1'], 'contains': ['144.u1.a1', '144.w1.a1', '144.w1.b1', '144.w1.c1', '192.c1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5925, -1, 6165, -1, 6997, -1, 3464, -1], 'generators': [87091200, 348, 160796595, 7625520], 'label': '1728.47489.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '1728.47489', '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': '24.12'}
  • id: 115937896
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.j1.a1'], 'contains': ['144.u1.a1', '144.x1.a1', '144.x1.b1', '144.x1.c1', '192.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5324, -1, 4595, -1, 7489, -1, 2194, -1], 'generators': [87091200, 348, 7625520, 160796618], 'label': '1728.47489.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.m1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115937897
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.k1.a1'], 'contains': ['144.v1.a1', '144.w1.a1', '144.x1.a1', '144.x1.b1', '192.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5439, -1, 5250, -1, 7744, -1, 2259, -1], 'generators': [87091200, 160796160, 7625520, 81], 'label': '1728.47489.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.n1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115937898
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.k1.b1'], 'contains': ['144.v1.a1', '144.w1.b1', '144.x1.b1', '144.x1.c1', '192.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5439, -1, 5106, -1, 7744, -1, 2595, -1], 'generators': [87091200, 160796595, 7625520, 81], 'label': '1728.47489.48.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.n1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937899
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1152.155790', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.b1.a1', '18.m1.a1', '18.m1.b1', '18.m1.c1', '24.j1.a1', '24.q1.a1', '24.q1.a2', '24.w1.a1', '24.w1.b1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2186, -1, 1086, -1, 7786, -1, 1984, -1], 'generators': [87091200, 40367945520, 348, 20801370240, 7625520, 6314117040, 160796618], 'label': '1728.47489.6.h1.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': '6.h1.a1', 'projective_image': '864.4709', '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': '48.50'}
  • id: 115937900
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.k1.c1'], 'contains': ['144.v1.a1', '144.w1.c1', '144.x1.a1', '144.x1.c1', '192.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5439, -1, 4545, -1, 7744, -1, 2325, -1], 'generators': [87091200, 7625520, 81, 51610035], 'label': '1728.47489.48.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.n1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937901
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.n1.a1'], 'contains': ['96.g1.a1', '144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.ba1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1472, -1, 2475, -1, 9166, -1, 800, -1], 'generators': [348, 81, 40364311680, 20757824640], 'label': '1728.47489.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.o1.a1', 'projective_image': '576.8487', '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': '3.1'}
  • id: 115937902
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.o1.a1'], 'contains': ['144.y1.a1', '144.bb1.a1', '144.bc1.c1', '144.bc1.c2', '192.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [166, -1, 1598, -1, 9689, -1, 682, -1], 'generators': [458, 160796160, 40364311680, 20757824640], 'label': '1728.47489.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.p1.a1', 'projective_image': '576.8487', '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': '12.3'}
  • id: 115937903
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.o1.b1'], 'contains': ['144.y1.a1', '144.bb1.b1', '144.bc1.a1', '144.bc1.a2', '192.b1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [166, -1, 792, -1, 9689, -1, 551, -1], 'generators': [458, 160796595, 40364311680, 20757824640], 'label': '1728.47489.48.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.p1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937904
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.o1.c1'], 'contains': ['144.y1.a1', '144.bb1.c1', '144.bc1.b1', '144.bc1.b2', '192.b1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [166, -1, 1918, -1, 9689, -1, 617, -1], 'generators': [458, 51610035, 40364311680, 20757824640], 'label': '1728.47489.48.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.p1.c1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937905
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.p1.a1'], 'contains': ['144.z1.a1', '144.bb1.a1', '144.bb1.b1', '144.bb1.c1', '192.c1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [995, -1, 1489, -1, 9562, -1, 748, -1], 'generators': [348, 160796595, 40364311680, 20757824640], 'label': '1728.47489.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.q1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115937906
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.q1.a1'], 'contains': ['144.z1.a1', '144.bc1.a1', '144.bc1.b1', '144.bc1.c1', '192.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [537, -1, 616, -1, 9944, -1, 28, -1], 'generators': [25916970240, 348, 32736493440, 160796618], 'label': '1728.47489.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.r1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115937907
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.q1.a2'], 'contains': ['144.z1.a1', '144.bc1.a2', '144.bc1.b2', '144.bc1.c2', '192.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [537, -1, 215, -1, 9944, -1, 94, -1], 'generators': [348, 40364311680, 160796618, 20757824640], 'label': '1728.47489.48.r1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.r1.a2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937908
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.a1'], 'contains': ['144.ba1.a1', '144.bb1.a1', '144.bc1.a1', '144.bc1.b2', '192.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 1183, -1, 9817, -1, 225, -1], 'generators': [160796160, 81, 40364311680, 20757824640], 'label': '1728.47489.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115937909
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.b1'], 'contains': ['144.ba1.b1', '144.bb1.a1', '144.bc1.a2', '144.bc1.b1', '192.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 1323, -1, 9817, -1, 159, -1], 'generators': [25916970240, 160796160, 32736493440, 81], 'label': '1728.47489.48.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937910
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.c1.a1', '18.l1.a1', '18.m1.a1', '18.m1.b1', '24.k1.a1', '24.r1.a1', '24.r1.b1', '24.x1.a1', '24.x1.b1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2029, -1, 2895, -1, 7963, -1, 2080, -1], 'generators': [87091200, 40367945520, 20801370240, 160796160, 7625520, 81, 6314117040], 'label': '1728.47489.6.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': '6.i1.a1', 'projective_image': '864.4709', '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': '48.50'}
  • id: 115937911
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.c1'], 'contains': ['144.ba1.a1', '144.bb1.b1', '144.bc1.b1', '144.bc1.c2', '192.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 1133, -1, 9817, -1, 421, -1], 'generators': [160796595, 81, 40364311680, 20757824640], 'label': '1728.47489.48.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937912
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.d1'], 'contains': ['144.ba1.b1', '144.bb1.b1', '144.bc1.b2', '144.bc1.c1', '192.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 1083, -1, 9817, -1, 486, -1], 'generators': [25916970240, 160796595, 32736493440, 81], 'label': '1728.47489.48.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.d1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937913
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.e1'], 'contains': ['144.ba1.a1', '144.bb1.c1', '144.bc1.a2', '144.bc1.c1', '192.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 484, -1, 9817, -1, 355, -1], 'generators': [81, 51610035, 40364311680, 20757824640], 'label': '1728.47489.48.s1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.e1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.e1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937914
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.r1.f1'], 'contains': ['144.ba1.b1', '144.bb1.c1', '144.bc1.a1', '144.bc1.c2', '192.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [50, -1, 286, -1, 9817, -1, 290, -1], 'generators': [25916970240, 32736493440, 81, 51610035], 'label': '1728.47489.48.s1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.s1.f1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937915
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '54.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['32.b1.a1', '32.b1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.c1.b1', '18.c1.c1', '18.l1.a1', '18.m1.a1', '18.m1.b1', '18.m1.c1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.b1.b1', '108.c1.a1', '108.g1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2709, 673, 4037, 1623, 5596, 9147, 5891, 1793], 'generators': [87091200, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.54.a1.a1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.c1.c1', '18.c1.b1'], 'normal_contains': ['216.a1.a1', '216.b1.a1', '216.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '864.4709', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115937916
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.a1', '108.f1.b1', '108.i1.b1', '108.j1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4536, -1, 7321, -1, 4033, -1, 7404, -1], 'generators': [7625520, 20805080339, 6314117040, 20757824640, 13941935280], 'label': '1728.47489.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '864.4709', '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': '32.27'}
  • id: 115937917
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 432, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.e1.b1', '27.a1.a1'], 'contains': ['108.b1.b1', '108.d1.a1', '108.f1.a1', '108.i1.a1', '108.j1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4536, -1, 7024, -1, 4033, -1, 7063, -1], 'generators': [90801299, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.54.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 115937918
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.e1.a1', '108.f1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6125, -1, 7484, -1, 3344, -1, 7589, -1], 'generators': [7625520, 6314117040, 11335619, 20757824640, 13941935280], 'label': '1728.47489.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115937919
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.b1', '18.g1.b1', '27.a1.a1'], 'contains': ['108.b1.b1', '108.e1.a1', '108.f1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6125, -1, 8136, -1, 3344, -1, 7816, -1], 'generators': [40367945520, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.54.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115937920
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.i1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.d1.a1', '108.e1.a1', '108.g1.a1', '108.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8441, -1, 8465, -1, 1909, -1, 7756, -1], 'generators': [87091200, 7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115937921
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.c1.b1', '18.l1.a1', '18.m1.b1', '18.m1.c1', '24.k1.b1', '24.r1.c1', '24.r1.d1', '24.x1.c1', '24.x1.d1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2029, -1, 2821, -1, 7963, -1, 2583, -1], 'generators': [87091200, 40367945520, 20801370240, 160796595, 7625520, 81, 6314117040], 'label': '1728.47489.6.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': '6.i1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 115937922
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.138', 'aut_weyl_index': 216, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.k1.a1', '27.a1.a1'], 'contains': ['108.f1.a1', '108.f1.b1', '108.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6719, -1, 7789, -1, 3681, -1, 7525, -1], 'generators': [87091200, 7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '864.4709', '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': '32.27'}
  • id: 115937923
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.c1.a1', '32.a1.a1', '32.b1.a1', '32.b1.a2'], 'contains': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '192.b1.c1', '192.c1.a1', '192.d1.a1', '192.e1.a1', '192.e1.b1', '192.e1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [958, -1, 4498, -1, 7408, -1, 3026, -1], 'generators': [348, 160796595, 81], 'label': '1728.47489.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '576.8487', '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': '2.1'}
  • id: 115937924
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.h1.a1', '24.h1.b1', '24.h1.c1', '36.o1.a1', '36.r1.a1'], 'contains': ['144.a1.a1', '144.t1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9129, 7996, 6650, 4878, 3559, 2441, 4979, 7309], 'generators': [87091200, 458, 7625520, 6314117040], 'label': '1728.47489.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1'], 'normal_contains': ['216.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937925
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.i1.a1', '24.j1.a1', '36.p1.a1', '36.s1.a1'], 'contains': ['144.b1.a1', '144.u1.a1', '216.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8694, 5818, 9411, 2486, 3410, 5924, 5095, 3927], 'generators': [87091200, 348, 7625520, 6314117040], 'label': '1728.47489.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['18.b1.a1', '24.a1.a1'], 'normal_contains': ['216.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937926
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.b1', 'complements': ['24.bb1.a1', '24.bb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.u1.a1', '24.u1.c1', '24.u1.e1', '36.c1.b1', '36.w1.a1'], 'contains': ['144.j1.a1', '216.b1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4015, 3780, 3292, 7189, 5463, 4183, 5398, 6156], 'generators': [458, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.72.c1.a1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['18.a1.a1', '24.b1.a1'], 'normal_contains': ['216.b1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937927
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': ['24.bb1.a1', '24.bb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.u1.b1', '24.u1.d1', '24.u1.f1', '36.c1.a1', '36.w1.b1'], 'contains': ['144.j1.b1', '216.b1.b1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4015, 3780, 4830, 8929, 5463, 4183, 5627, 8462], 'generators': [458, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.c1.b1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '72.c1.b1', 'normal_contained_in': ['18.a1.a1', '24.b1.b1'], 'normal_contains': ['216.b1.b1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.b1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937928
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.b1', 'complements': ['24.ba1.c1', '24.ba1.d1', '24.ba1.e1', '24.ba1.f1', '24.ba1.a1', '24.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.v1.a1', '24.w1.a1', '36.d1.b1', '36.x1.a1'], 'contains': ['144.k1.a1', '216.b1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3163, 1880, 3509, 3682, 5870, 7666, 5731, 2774], 'generators': [40367945520, 348, 20801370240, 6314117040], 'label': '1728.47489.72.d1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.d1.a1', 'normal_contained_in': ['18.b1.a1', '24.b1.a1'], 'normal_contains': ['216.b1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937929
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': ['24.ba1.c1', '24.ba1.d1', '24.ba1.e1', '24.ba1.f1', '24.ba1.a1', '24.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.v1.b1', '24.w1.b1', '36.d1.a1', '36.x1.b1'], 'contains': ['144.k1.b1', '216.b1.b1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3163, 1880, 5629, 6074, 5870, 7666, 6688, 5081], 'generators': [348, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.d1.b1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.d1.b1', 'normal_contained_in': ['18.b1.a1', '24.b1.b1'], 'normal_contains': ['216.b1.b1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.b1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937930
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.c1.b1', '36.f1.a1', '36.o1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.j1.a1', '216.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4750, -1, 7675, -1, 4297, -1, 7248, -1], 'generators': [458, 40367945520, 7625520, 6314117040], 'label': '1728.47489.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937931
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '36.c1.a1', '36.f1.a1', '36.o1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.j1.b1', '216.c1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4750, -1, 7781, -1, 4297, -1, 7381, -1], 'generators': [87091200, 458, 20797746480, 6314117040], 'label': '1728.47489.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.e1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937932
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.c1.c1', '18.l1.a1', '18.m1.a1', '18.m1.c1', '24.k1.c1', '24.r1.e1', '24.r1.f1', '24.x1.e1', '24.x1.f1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2029, -1, 944, -1, 7963, -1, 2298, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 81, 51610035, 6314117040], 'label': '1728.47489.6.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.i1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.c1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 115937933
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.d1.b1', '36.g1.a1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.e1.a1', '144.k1.a1', '216.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3628, -1, 8226, -1, 4168, -1, 8642, -1], 'generators': [40367945520, 348, 7625520, 6314117040], 'label': '1728.47489.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115937934
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '36.d1.a1', '36.g1.a1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.e1.a1', '144.k1.b1', '216.c1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3628, -1, 9160, -1, 4168, -1, 8709, -1], 'generators': [87091200, 348, 20797746480, 6314117040], 'label': '1728.47489.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.f1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937935
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.b1', '36.h1.b1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.l1.a1', '216.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2770, -1, 5563, -1, 6000, -1, 6087, -1], 'generators': [40367945520, 7625520, 81, 6314117040], 'label': '1728.47489.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '864.4709', '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: 115937936
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.b1', '36.h1.a1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.f1.b1', '144.l1.a1', '216.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2770, -1, 5513, -1, 6000, -1, 6153, -1], 'generators': [83467440, 40367945520, 81, 6314117040], 'label': '1728.47489.72.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.g1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937937
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '36.e1.a1', '36.h1.b1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.l1.b1', '216.c1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2770, -1, 5916, -1, 6000, -1, 6365, -1], 'generators': [87091200, 81, 13945559040, 6314117040], 'label': '1728.47489.72.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.g1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937938
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '36.e1.a1', '36.h1.a1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.f1.b1', '144.l1.b1', '216.c1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2770, -1, 5822, -1, 6000, -1, 6508, -1], 'generators': [87091200, 20797746480, 81, 6314117040], 'label': '1728.47489.72.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.g1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937939
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.a1.a1', '36.f1.a1', '36.o1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.m1.a1', '216.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7586, -1, 8959, -1, 2293, -1, 8780, -1], 'generators': [87091200, 458, 40364311680, 6314117040], 'label': '1728.47489.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.h1.a1', 'projective_image': '288.1036', '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': '8.3'}
  • id: 115937940
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1', '36.g1.a1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.e1.a1', '144.n1.a1', '216.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7292, -1, 9470, -1, 2144, -1, 9090, -1], 'generators': [87091200, 348, 40364311680, 6314117040], 'label': '1728.47489.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.a1', 'projective_image': '864.4709', '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': '8.3'}
  • id: 115937941
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.h1.a1', '36.h1.b1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.f1.b1', '144.o1.a1', '216.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6433, -1, 4014, -1, 5170, -1, 6436, -1], 'generators': [87091200, 81, 40364311680, 6314117040], 'label': '1728.47489.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '864.4709', '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: 115937942
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.a1.a1', '36.i1.a1', '36.r1.a1'], 'contains': ['144.a1.a1', '144.g1.a1', '144.p1.a1', '144.p2.a1', '216.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8562, -1, 8900, -1, 1286, -1, 8274, -1], 'generators': [90801299, 458, 7625520, 6314117040], 'label': '1728.47489.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '72.k1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937943
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['16.b1.a1', '24.a1.a1', '24.h1.a1', '24.h1.b1', '24.h1.c1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.k1.b1', '24.k1.c1', '32.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5163, -1, 4758, -1, 7350, -1, 3048, -1], 'generators': [87091200, 348, 160796595, 7625520, 81, 6314117040], 'label': '1728.47489.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '288.1036', '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': '24.12'}
  • id: 115937944
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.b1.a1', '36.j1.a1', '36.s1.a1'], 'contains': ['144.b1.a1', '144.h1.a1', '144.q1.a1', '144.q2.a1', '216.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8204, -1, 9339, -1, 1137, -1, 8935, -1], 'generators': [90801299, 348, 7625520, 6314117040], 'label': '1728.47489.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.l1.a1', 'projective_image': '864.4709', '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': '24.14'}
  • id: 115937945
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.c1.a1', '36.c1.b1', '36.i1.a1', '36.k1.a1', '36.l1.a1', '36.l1.b1', '36.o1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.j1.b1', '216.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7029, -1, 8030, -1, 2726, -1, 7520, -1], 'generators': [458, 7625520, 6314117040, 13941935280], 'label': '1728.47489.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.m1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937946
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.a1.a1', '36.k1.a1', '36.r1.a1'], 'contains': ['144.a1.a1', '144.r1.a1', '144.r1.b1', '216.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9643, -1, 9264, -1, 729, -1, 9013, -1], 'generators': [458, 7625520, 6314117040, 11335619], 'label': '1728.47489.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '72.n1.a1', 'projective_image': '288.1036', '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': '2.1'}
  • id: 115937947
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.d1.a1', '36.d1.b1', '36.j1.a1', '36.m1.a1', '36.n1.a1', '36.n1.b1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.k1.a1', '144.k1.b1', '216.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6762, -1, 9033, -1, 2572, -1, 8857, -1], 'generators': [348, 7625520, 6314117040, 13941935280], 'label': '1728.47489.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.o1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115937948
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.b1.a1', '36.m1.a1', '36.s1.a1'], 'contains': ['144.b1.a1', '144.s1.a1', '144.s1.b1', '216.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9265, -1, 9731, -1, 573, -1, 9249, -1], 'generators': [348, 7625520, 6314117040, 11335619], 'label': '1728.47489.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.p1.a1', 'projective_image': '864.4709', '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': '12.4'}
  • id: 115937949
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.e1.a1', '36.e1.b1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.l1.a1', '144.l1.b1', '216.f1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6265, -1, 5987, -1, 5321, -1, 6292, -1], 'generators': [7625520, 81, 6314117040, 13941935280], 'label': '1728.47489.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.q1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115937950
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.k1.a1', '24.k1.b1', '24.k1.c1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.v1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7719, -1, 4690, -1, 5731, -1, 2901, -1], 'generators': [87091200, 7625520, 81, 6314117040], 'label': '1728.47489.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937951
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '36.t1.a1'], 'contains': ['144.w1.a1', '216.a1.a1', '288.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5405, -1, 5170, -1, 7617, -1, 3361, -1], 'generators': [87091200, 160796160, 7625520, 6314117040], 'label': '1728.47489.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.s1.a1', 'projective_image': '864.4709', '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': '24.12'}
  • id: 115937952
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '24.h1.b1', '24.i1.a1', '24.k1.b1', '36.t1.b1'], 'contains': ['144.w1.b1', '216.a1.a1', '288.d1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5405, -1, 4940, -1, 7617, -1, 3948, -1], 'generators': [87091200, 160796595, 7625520, 6314117040], 'label': '1728.47489.72.s1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.s1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937953
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.c1', '24.h1.c1', '24.i1.a1', '24.k1.c1', '36.t1.c1'], 'contains': ['144.w1.c1', '216.a1.a1', '288.d1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5405, -1, 5038, -1, 7617, -1, 3296, -1], 'generators': [87091200, 7625520, 51610035, 6314117040], 'label': '1728.47489.72.s1.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.s1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937954
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['16.c1.a1', '24.n1.a1', '24.o1.a1', '24.o1.b1', '24.o1.c1', '24.p1.a1', '24.q1.a1', '24.q1.a2', '24.r1.a1', '24.r1.b1', '24.r1.c1', '24.r1.d1', '24.r1.e1', '24.r1.f1', '32.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [875, -1, 2590, -1, 9014, -1, 1130, -1], 'generators': [348, 160796595, 81, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937955
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.h1.b1', '24.j1.a1', '24.k1.a1', '24.k1.c1'], 'contains': ['144.x1.a1', '216.a1.a1', '288.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5138, -1, 3119, -1, 7945, -1, 1988, -1], 'generators': [87091200, 7625520, 160796430, 6314117040], 'label': '1728.47489.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937956
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '24.h1.c1', '24.j1.a1', '24.k1.a1', '24.k1.b1'], 'contains': ['144.x1.b1', '216.a1.a1', '288.e1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5138, -1, 3729, -1, 7945, -1, 2109, -1], 'generators': [160796241, 87091200, 7625520, 6314117040], 'label': '1728.47489.72.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.t1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937957
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.c1', '24.h1.a1', '24.j1.a1', '24.k1.b1', '24.k1.c1'], 'contains': ['144.x1.c1', '216.a1.a1', '288.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5138, -1, 3064, -1, 7945, -1, 2409, -1], 'generators': [87091200, 7625520, 6314117040, 160796618], 'label': '1728.47489.72.t1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.t1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937958
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.c1.a1', '36.c1.b1', '36.f1.a1'], 'contains': ['144.d1.a1', '144.j1.a1', '144.j1.b1', '216.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4174, -1, 7368, -1, 5019, -1, 7074, -1], 'generators': [458, 40367945520, 20797746480, 6314117040], 'label': '1728.47489.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.u1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937959
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.d1.a1', '36.d1.b1', '36.g1.a1'], 'contains': ['144.e1.a1', '144.k1.a1', '144.k1.b1', '216.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2644, -1, 8093, -1, 4777, -1, 8463, -1], 'generators': [40367945520, 348, 20797746480, 6314117040], 'label': '1728.47489.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.v1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115937960
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.e1.a1', '36.e1.b1', '36.h1.b1'], 'contains': ['144.f1.a1', '144.l1.a1', '144.l1.b1', '216.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2080, -1, 5442, -1, 6271, -1, 5935, -1], 'generators': [40367945520, 20761458480, 81, 6314117040], 'label': '1728.47489.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.w1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115937961
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.e1.a1', '36.e1.b1', '36.h1.a1'], 'contains': ['144.f1.b1', '144.l1.a1', '144.l1.b1', '216.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2080, -1, 5367, -1, 6271, -1, 6014, -1], 'generators': [40367945520, 20797746480, 81, 6314117040], 'label': '1728.47489.72.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.w1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937962
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.c1.b1', '36.f1.a1', '36.u1.a1'], 'contains': ['144.d1.a1', '144.j1.a1', '216.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4398, -1, 7001, -1, 4635, -1, 6958, -1], 'generators': [458, 20797746480, 6314117040, 13941935280], 'label': '1728.47489.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.x1.a1', 'projective_image': '288.1036', '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': '8.3'}
  • id: 115937963
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '36.c1.a1', '36.f1.a1', '36.u1.b1'], 'contains': ['144.d1.a1', '144.j1.b1', '216.i1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4398, -1, 7568, -1, 4635, -1, 7315, -1], 'generators': [458, 20797746480, 6314117040, 40443787440], 'label': '1728.47489.72.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.x1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115937964
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.d1.b1', '36.g1.a1', '36.v1.a1'], 'contains': ['144.e1.a1', '144.k1.a1', '216.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2886, -1, 7439, -1, 4427, -1, 8390, -1], 'generators': [348, 20797746480, 6314117040, 13941935280], 'label': '1728.47489.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.y1.a1', 'projective_image': '864.4709', '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': '8.3'}
  • id: 115937965
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['24.b1.a1', '24.u1.a1', '24.u1.c1', '24.u1.e1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '24.x1.c1', '24.x1.e1', '32.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1902, -1, 2507, -1, 7843, -1, 3185, -1], 'generators': [40367945520, 348, 20801370240, 160796595, 81, 6314117040], 'label': '1728.47489.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.c1.a1', 'projective_image': '288.1036', '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': '24.12'}
  • id: 115937966
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '36.d1.a1', '36.g1.a1', '36.v1.b1'], 'contains': ['144.e1.a1', '144.k1.b1', '216.i1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2886, -1, 8754, -1, 4427, -1, 8536, -1], 'generators': [348, 20797746480, 6314117040, 40443787440], 'label': '1728.47489.72.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.y1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115937967
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.e1.b1', '36.h1.a1', '36.h1.b1'], 'contains': ['144.f1.a1', '144.f1.b1', '144.l1.a1', '216.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2271, -1, 3909, -1, 6129, -1, 5863, -1], 'generators': [20797746480, 81, 6314117040, 13941935280], 'label': '1728.47489.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.z1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115937968
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '36.e1.a1', '36.h1.a1', '36.h1.b1'], 'contains': ['144.f1.a1', '144.f1.b1', '144.l1.b1', '216.i1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2271, -1, 3959, -1, 6129, -1, 6220, -1], 'generators': [20797746480, 81, 6314117040, 40443787440], 'label': '1728.47489.72.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.z1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937969
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.o1.a1', '24.o1.b1', '24.o1.c1', '36.f1.a1'], 'contains': ['144.d1.a1', '144.y1.a1', '216.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1912, -1, 2727, -1, 8647, -1, 1862, -1], 'generators': [458, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '288.1036', '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': '12.3'}
  • id: 115937970
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.p1.a1', '24.q1.a1', '24.q1.a2', '36.g1.a1'], 'contains': ['144.e1.a1', '144.z1.a1', '216.j1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1473, -1, 2507, -1, 8796, -1, 1749, -1], 'generators': [348, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bb1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937971
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.r1.a1', '24.r1.c1', '24.r1.e1', '36.h1.b1'], 'contains': ['144.f1.a1', '144.ba1.a1', '216.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1308, -1, 2195, -1, 8981, -1, 1447, -1], 'generators': [81, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.bc1.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': '72.bc1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937972
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.r1.b1', '24.r1.d1', '24.r1.f1', '36.h1.a1'], 'contains': ['144.f1.b1', '144.ba1.b1', '216.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1308, -1, 2136, -1, 8981, -1, 1523, -1], 'generators': [20797746480, 81, 6314117040, 13905647280], 'label': '1728.47489.72.bc1.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': '72.bc1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937973
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '24.o1.a1', '24.p1.a1', '24.r1.a1', '24.r1.b1'], 'contains': ['144.bb1.a1', '216.j1.a1', '288.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [478, -1, 2292, -1, 9270, -1, 1320, -1], 'generators': [160796160, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.bd1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937974
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '24.o1.b1', '24.p1.a1', '24.r1.c1', '24.r1.d1'], 'contains': ['144.bb1.b1', '216.j1.a1', '288.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [478, -1, 1621, -1, 9270, -1, 1678, -1], 'generators': [160796595, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.bd1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937975
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.c1', '24.o1.c1', '24.p1.a1', '24.r1.e1', '24.r1.f1'], 'contains': ['144.bb1.c1', '216.j1.a1', '288.d1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [478, -1, 2067, -1, 9270, -1, 1594, -1], 'generators': [51610035, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.bd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.bd1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937976
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.b1'], 'contains': ['24.b1.b1', '24.u1.b1', '24.u1.d1', '24.u1.f1', '24.v1.b1', '24.w1.b1', '24.x1.b1', '24.x1.d1', '24.x1.f1', '32.a1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1902, -1, 3366, -1, 7843, -1, 4107, -1], 'generators': [348, 160796595, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.c1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937977
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.o1.b1', '24.q1.a1', '24.r1.a1', '24.r1.f1'], 'contains': ['144.bc1.a1', '216.j1.a1', '288.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 766, -1, 9397, -1, 890, -1], 'generators': [20797746480, 160796430, 6314117040, 13905647280], 'label': '1728.47489.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937978
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.o1.b1', '24.q1.a2', '24.r1.b1', '24.r1.e1'], 'contains': ['144.bc1.a2', '216.j1.a1', '288.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 672, -1, 9397, -1, 974, -1], 'generators': [160796430, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.be1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.a2', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937979
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '24.o1.c1', '24.q1.a1', '24.r1.b1', '24.r1.c1'], 'contains': ['144.bc1.b1', '216.j1.a1', '288.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 1907, -1, 9397, -1, 1040, -1], 'generators': [160796241, 20797746480, 6314117040, 13905647280], 'label': '1728.47489.72.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937980
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '24.o1.c1', '24.q1.a2', '24.r1.a1', '24.r1.d1'], 'contains': ['144.bc1.b2', '216.j1.a1', '288.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 1685, -1, 9397, -1, 1105, -1], 'generators': [160796241, 40364311680, 6314117040, 20757824640], 'label': '1728.47489.72.be1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.b2', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.b2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937981
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.c1', '24.o1.a1', '24.q1.a1', '24.r1.d1', '24.r1.e1'], 'contains': ['144.bc1.c1', '216.j1.a1', '288.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 474, -1, 9397, -1, 1236, -1], 'generators': [20797746480, 6314117040, 13905647280, 160796618], 'label': '1728.47489.72.be1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937982
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.c1', '24.o1.a1', '24.q1.a2', '24.r1.c1', '24.r1.f1'], 'contains': ['144.bc1.c2', '216.j1.a1', '288.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [270, -1, 127, -1, 9397, -1, 1171, -1], 'generators': [40364311680, 6314117040, 160796618, 20757824640], 'label': '1728.47489.72.be1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '72.be1.c2', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.c2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937983
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.i1.a1', '36.u1.a1', '36.w1.a1'], 'contains': ['144.g1.a1', '144.j1.a1', '216.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5946, -1, 6748, -1, 2952, -1, 6892, -1], 'generators': [90801299, 458, 6314117040, 13941935280], 'label': '1728.47489.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '72.bf1.a1', 'projective_image': '288.1036', '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': '8.3'}
  • id: 115937984
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '36.i1.a1', '36.u1.b1', '36.w1.b1'], 'contains': ['144.g1.a1', '144.j1.b1', '216.k1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5946, -1, 8347, -1, 2952, -1, 7447, -1], 'generators': [90801299, 458, 13945559040, 6314117040], 'label': '1728.47489.72.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.bf1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115937985
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.j1.a1', '36.v1.a1', '36.x1.a1'], 'contains': ['144.h1.a1', '144.k1.a1', '216.k1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5661, -1, 7223, -1, 2845, -1, 8126, -1], 'generators': [90801299, 348, 6314117040, 13941935280], 'label': '1728.47489.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.bg1.a1', 'projective_image': '864.4709', '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': '24.8'}
  • id: 115937986
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '36.j1.a1', '36.v1.b1', '36.x1.b1'], 'contains': ['144.h1.a1', '144.k1.b1', '216.k1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5661, -1, 8536, -1, 2845, -1, 8215, -1], 'generators': [90801299, 348, 13945559040, 6314117040], 'label': '1728.47489.72.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.bg1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 115937987
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6912.ds', 'aut_weyl_index': 2, 'centralizer': '288.a1.a1', 'complements': ['576.a1.a1', '576.c1.a1', '576.e1.b1', '576.e1.a1', '576.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '9.b1.a1', '9.c1.a1', '9.c1.b1', '9.c1.c1', '12.j1.a1', '12.n1.a1', '12.n1.b1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4715, 1282, 4540, 793, 6703, 8590, 5758, 1526], 'generators': [87091200, 40367945520, 348, 20801370240, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '864.4709', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1036'}
  • id: 115937988
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '24.z1.a1', '24.ba1.a1', '24.ba1.c1', '24.ba1.e1', '24.bb1.a1', '32.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5740, -1, 6226, -1, 6352, -1, 3907, -1], 'generators': [87091200, 348, 160796595, 7625520, 81, 11335619], 'label': '1728.47489.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '576.8487', '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': '72.43'}
  • id: 115937989
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '72.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.l1.a1', '36.u1.a1', '36.w1.a1'], 'contains': ['144.j1.a1', '216.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4623, -1, 7078, -1, 3968, -1, 7013, -1], 'generators': [458, 40440078659, 6314117040, 13941935280], 'label': '1728.47489.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '72.bh1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115937990
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '72.bh1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '36.l1.b1', '36.u1.b1', '36.w1.b1'], 'contains': ['144.j1.b1', '216.l1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4623, -1, 7981, -1, 3968, -1, 7629, -1], 'generators': [40356979139, 458, 13945559040, 6314117040], 'label': '1728.47489.72.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.bh1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115937991
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.n1.a1', '36.v1.a1', '36.x1.a1'], 'contains': ['144.k1.a1', '216.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3854, -1, 7496, -1, 3138, -1, 8171, -1], 'generators': [348, 40440078659, 6314117040, 13941935280], 'label': '1728.47489.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.bi1.a1', 'projective_image': '864.4709', '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': '24.14'}
  • id: 115937992
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '36.n1.b1', '36.v1.b1', '36.x1.b1'], 'contains': ['144.k1.b1', '216.l1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3854, -1, 8826, -1, 3138, -1, 8335, -1], 'generators': [40356979139, 348, 13945559040, 6314117040], 'label': '1728.47489.72.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.bi1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115937993
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.x1.a1', '24.x1.c1', '24.x1.e1', '36.e1.b1'], 'contains': ['144.l1.a1', '216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2452, -1, 990, -1, 6413, -1, 3780, -1], 'generators': [40367945520, 20801370240, 81, 6314117040], 'label': '1728.47489.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bj1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115937994
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.x1.b1', '24.x1.d1', '24.x1.f1', '36.e1.a1'], 'contains': ['144.l1.b1', '216.b1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2452, -1, 3169, -1, 6413, -1, 4259, -1], 'generators': [81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bj1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115937995
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '24.u1.a1', '24.v1.a1', '24.x1.a1', '36.y1.a1'], 'contains': ['216.b1.a1', '288.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 2414, -1, 8086, -1, 3876, -1], 'generators': [40367945520, 20801370240, 160796160, 6314117040], 'label': '1728.47489.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.bk1.a1', 'projective_image': '864.4709', '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': '24.12'}
  • id: 115937996
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '24.u1.b1', '24.v1.b1', '24.x1.b1', '36.y1.b1'], 'contains': ['216.b1.b1', '288.d1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 4233, -1, 8086, -1, 4355, -1], 'generators': [160796160, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bk1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '72.bk1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937997
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '24.u1.c1', '24.v1.a1', '24.x1.c1', '36.y1.c1'], 'contains': ['216.b1.a1', '288.d1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 1768, -1, 8086, -1, 4662, -1], 'generators': [40367945520, 20801370240, 160796595, 6314117040], 'label': '1728.47489.72.bk1.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.bk1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937998
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '24.u1.d1', '24.v1.b1', '24.x1.d1', '36.y1.d1'], 'contains': ['216.b1.b1', '288.d1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 3394, -1, 8086, -1, 4789, -1], 'generators': [160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bk1.d1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '72.bk1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115937999
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '24.z1.b1', '24.ba1.b1', '24.ba1.d1', '24.ba1.f1', '24.bb1.b1', '32.b1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5740, -1, 6050, -1, 6352, -1, 3826, -1], 'generators': [87091200, 6321450899, 348, 160796595, 7625520, 81], 'label': '1728.47489.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 115938000
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.c1', '24.u1.e1', '24.v1.a1', '24.x1.e1', '36.y1.e1'], 'contains': ['216.b1.a1', '288.d1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 2825, -1, 8086, -1, 3835, -1], 'generators': [40367945520, 20801370240, 51610035, 6314117040], 'label': '1728.47489.72.bk1.e1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.bk1.e1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938001
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.c1', '24.u1.f1', '24.v1.b1', '24.x1.f1', '36.y1.f1'], 'contains': ['216.b1.b1', '288.d1.c1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 4172, -1, 8086, -1, 4313, -1], 'generators': [51610035, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bk1.f1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '72.bk1.f1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938002
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.u1.c1', '24.w1.a1', '24.x1.a1', '24.x1.e1'], 'contains': ['216.b1.a1', '288.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 589, -1, 8460, -1, 2463, -1], 'generators': [40367945520, 20801370240, 160796430, 6314117040], 'label': '1728.47489.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '72.bl1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115938003
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '24.u1.d1', '24.w1.b1', '24.x1.b1', '24.x1.f1'], 'contains': ['216.b1.b1', '288.e1.a1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 1452, -1, 8460, -1, 2745, -1], 'generators': [160796430, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '72.bl1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938004
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '24.u1.e1', '24.w1.a1', '24.x1.a1', '24.x1.c1'], 'contains': ['216.b1.a1', '288.e1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 821, -1, 8460, -1, 2523, -1], 'generators': [160796241, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.72.bl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '72.bl1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938005
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.b1', '24.u1.f1', '24.w1.b1', '24.x1.b1', '24.x1.d1'], 'contains': ['216.b1.b1', '288.e1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 2667, -1, 8460, -1, 2806, -1], 'generators': [160796241, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.72.bl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '72.bl1.d1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938006
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.c1', '24.u1.a1', '24.w1.a1', '24.x1.c1', '24.x1.e1'], 'contains': ['216.b1.a1', '288.e1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 13, -1, 8460, -1, 2685, -1], 'generators': [40367945520, 20801370240, 6314117040, 160796618], 'label': '1728.47489.72.bl1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '72.bl1.e1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.e1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938007
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.c1', '24.u1.b1', '24.w1.b1', '24.x1.d1', '24.x1.f1'], 'contains': ['216.b1.b1', '288.e1.c1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1673, -1, 1282, -1, 8460, -1, 2961, -1], 'generators': [13945559040, 6314117040, 160796618, 40443787440], 'label': '1728.47489.72.bl1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.b1', 'old_label': '72.bl1.f1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938008
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.a1.a1'], 'contains': ['144.m1.a1', '144.p1.a1', '144.r1.a1', '216.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9770, -1, 9581, -1, 302, -1, 9575, -1], 'generators': [458, 7625520, 11335619, 13905647280], 'label': '1728.47489.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.bm1.a1', 'projective_image': '576.8487', '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': '4.2'}
  • id: 115938009
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.b1', '36.a1.a1'], 'contains': ['144.m1.a1', '144.p1.a1', '144.r1.b1', '216.m1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9770, -1, 9633, -1, 302, -1, 9642, -1], 'generators': [6321450899, 458, 7625520, 13905647280], 'label': '1728.47489.72.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.bm1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938010
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 54, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1', '3.c1.b1', '3.c1.c1'], 'contains': ['18.a1.a1', '18.d1.a1', '18.d1.b1', '18.f1.a1', '18.f1.b1', '18.h1.a1', '18.j1.a1', '27.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6268, -1, 7159, -1, 3761, -1, 7323, -1], 'generators': [87091200, 458, 40367945520, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '288.1036', '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': '32.27'}
  • id: 115938011
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.b1.a1'], 'contains': ['144.n1.a1', '144.q1.a1', '144.s1.a1', '216.m1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8928, -1, 9922, -1, 35, -1, 9697, -1], 'generators': [348, 7625520, 11335619, 13905647280], 'label': '1728.47489.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.bn1.a1', 'projective_image': '1728.47489', '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': '12.4'}
  • id: 115938012
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.b1', '36.b1.a1'], 'contains': ['144.n1.a1', '144.q1.a1', '144.s1.b1', '216.m1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8928, -1, 9987, -1, 35, -1, 9742, -1], 'generators': [6321450899, 348, 7625520, 13905647280], 'label': '1728.47489.72.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.bn1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115938013
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.ba1.a1', '24.ba1.c1', '24.ba1.e1', '36.r1.a1'], 'contains': ['144.p2.a1', '144.r1.a1', '144.t1.a1', '216.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9950, -1, 6892, -1, 1590, -1, 4735, -1], 'generators': [87091200, 458, 7625520, 11335619], 'label': '1728.47489.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '72.bo1.a1', 'projective_image': '576.8487', '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': '4.2'}
  • id: 115938014
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.b1', '24.ba1.b1', '24.ba1.d1', '24.ba1.f1', '36.r1.a1'], 'contains': ['144.p2.a1', '144.r1.b1', '144.t1.a1', '216.n1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9950, -1, 6827, -1, 1590, -1, 4500, -1], 'generators': [87091200, 6321450899, 458, 7625520], 'label': '1728.47489.72.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '72.bo1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938015
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.bb1.a1', '36.s1.a1'], 'contains': ['144.q2.a1', '144.s1.a1', '144.u1.a1', '216.n1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9439, -1, 9217, -1, 1482, -1, 5498, -1], 'generators': [87091200, 348, 7625520, 11335619], 'label': '1728.47489.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '72.bp1.a1', 'projective_image': '1728.47489', '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': '12.4'}
  • id: 115938016
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 576, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.b1', '24.bb1.b1', '36.s1.a1'], 'contains': ['144.q2.a1', '144.s1.b1', '144.u1.a1', '216.n1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9439, -1, 8698, -1, 1482, -1, 5453, -1], 'generators': [87091200, 6321450899, 348, 7625520], 'label': '1728.47489.72.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '72.bp1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115938017
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bb1.a1', '36.t1.a1'], 'contains': ['144.w1.a1', '216.n1.a1', '288.n1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6440, -1, 6548, -1, 3693, -1], 'generators': [87091200, 160796160, 7625520, 11335619], 'label': '1728.47489.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '72.bq1.a1', 'projective_image': '1728.47489', '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': '24.12'}
  • id: 115938018
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.b1', '24.bb1.b1', '36.t1.a1'], 'contains': ['144.w1.a1', '216.n1.b1', '288.n1.a2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6298, -1, 6548, -1, 3658, -1], 'generators': [87091200, 6321450899, 160796160, 7625520], 'label': '1728.47489.72.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '72.bq1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938019
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.c1', '24.bb1.a1', '36.t1.b1'], 'contains': ['144.w1.b1', '216.n1.a1', '288.n1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6099, -1, 6548, -1, 4569, -1], 'generators': [87091200, 160796595, 7625520, 11335619], 'label': '1728.47489.72.bq1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '72.bq1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938020
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.d1', '24.bb1.b1', '36.t1.b1'], 'contains': ['144.w1.b1', '216.n1.b1', '288.n1.b2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6045, -1, 6548, -1, 4449, -1], 'generators': [87091200, 6321450899, 160796595, 7625520], 'label': '1728.47489.72.bq1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '72.bq1.d1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938021
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1036279', 'aut_weyl_index': 18, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1', '18.e1.a1', '18.e1.b1', '18.g1.a1', '18.g1.b1', '18.i1.a1', '18.k1.a1', '27.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6141, -1, 8047, -1, 3618, -1, 8651, -1], 'generators': [87091200, 40367945520, 348, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '864.4709', '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': '96.160'}
  • id: 115938022
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.e1', '24.bb1.a1', '36.t1.c1'], 'contains': ['144.w1.c1', '216.n1.a1', '288.n1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6411, -1, 6548, -1, 3604, -1], 'generators': [87091200, 7625520, 51610035, 11335619], 'label': '1728.47489.72.bq1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '72.bq1.e1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938023
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.f1', '24.bb1.b1', '36.t1.c1'], 'contains': ['144.w1.c1', '216.n1.b1', '288.n1.c2'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5793, -1, 6168, -1, 6548, -1, 3551, -1], 'generators': [87091200, 6321450899, 7625520, 51610035], 'label': '1728.47489.72.bq1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '72.bq1.f1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938024
    {'ambient': '1728.47489', 'aut_centralizer_order': 3456, 'aut_label': '96.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.f1.a1', '48.f1.b1'], 'contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1', '288.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6043, 9327, 8124, 8060, 3779, 699, 7533, 9537], 'generators': [348, 81, 6314117040], 'label': '1728.47489.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '24.b1.b1'], 'normal_contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.50', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938025
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.o1.a1', '24.u1.a1', '24.u1.b1', '32.a1.a1', '48.d1.a1'], 'contains': ['192.b1.a1', '288.a1.a1', '288.d1.a1', '288.e1.c1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1002, -1, 3538, -1, 7862, -1, 3188, -1], 'generators': [458, 160796160, 6314117040], 'label': '1728.47489.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '288.1036', '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': '2.1'}
  • id: 115938026
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.o1.b1', '24.u1.c1', '24.u1.d1', '32.a1.a1', '48.d1.b1'], 'contains': ['192.b1.b1', '288.a1.a1', '288.d1.b1', '288.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1002, -1, 3134, -1, 7862, -1, 3989, -1], 'generators': [458, 160796595, 6314117040], 'label': '1728.47489.96.b1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.b1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938027
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.c1', '24.o1.c1', '24.u1.e1', '24.u1.f1', '32.a1.a1', '48.d1.c1'], 'contains': ['192.b1.c1', '288.a1.a1', '288.d1.c1', '288.e1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1002, -1, 3646, -1, 7862, -1, 3086, -1], 'generators': [458, 51610035, 6314117040], 'label': '1728.47489.96.b1.c1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.b1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938028
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.p1.a1', '24.v1.a1', '24.v1.b1', '32.a1.a1', '48.e1.a1'], 'contains': ['192.c1.a1', '288.b1.a1', '288.d1.a1', '288.d1.b1', '288.d1.c1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2088, -1, 3474, -1, 7685, -1, 3796, -1], 'generators': [348, 160796595, 6314117040], 'label': '1728.47489.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '864.4709', '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': '2.1'}
  • id: 115938029
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.q1.a1', '24.q1.a2', '24.w1.a1', '24.w1.b1', '32.a1.a1'], 'contains': ['192.d1.a1', '288.b1.a1', '288.e1.a1', '288.e1.b1', '288.e1.c1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1244, -1, 651, -1, 8072, -1, 2168, -1], 'generators': [348, 6314117040, 160796618], 'label': '1728.47489.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '96.d1.a1', 'projective_image': '864.4709', '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': '1.1'}
  • id: 115938030
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.r1.a1', '24.r1.b1', '24.x1.a1', '24.x1.b1', '32.a1.a1'], 'contains': ['192.e1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.e1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [680, -1, 3012, -1, 8201, -1, 2307, -1], 'generators': [160796160, 81, 6314117040], 'label': '1728.47489.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '96.e1.a1', 'projective_image': '864.4709', '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': '1.1'}
  • id: 115938031
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.r1.c1', '24.r1.d1', '24.x1.c1', '24.x1.d1', '32.a1.a1'], 'contains': ['192.e1.b1', '288.c1.a1', '288.d1.b1', '288.e1.b1', '288.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [680, -1, 2325, -1, 8201, -1, 2728, -1], 'generators': [160796595, 81, 6314117040], 'label': '1728.47489.96.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '96.e1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938032
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.c1.a1', '27.a1.a1', '36.t1.a1', '36.y1.a1', '36.y1.b1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4571, -1, 5134, -1, 6802, -1, 5752, -1], 'generators': [87091200, 40367945520, 20801370240, 160796160, 7625520, 6314117040, 11335619], 'label': '1728.47489.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '864.4709', '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': '96.227'}
  • id: 115938033
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.c1', '24.r1.e1', '24.r1.f1', '24.x1.e1', '24.x1.f1', '32.a1.a1'], 'contains': ['192.e1.c1', '288.c1.a1', '288.d1.c1', '288.e1.a1', '288.e1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [680, -1, 275, -1, 8201, -1, 2481, -1], 'generators': [81, 51610035, 6314117040], 'label': '1728.47489.96.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '96.e1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938034
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.g1.a1', '48.h1.a1', '48.h2.a1', '48.i1.a1', '48.i1.b1', '48.j1.a1'], 'contains': ['192.a1.a1', '288.f1.a1', '288.g1.a1', '288.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7907, -1, 9693, -1, 1951, -1, 8674, -1], 'generators': [348, 7625520, 81], 'label': '1728.47489.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '96.f1.a1', 'projective_image': '576.8487', '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': '2.1'}
  • id: 115938035
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.g1.a1', '48.o1.a1'], 'contains': ['192.a1.a1', '288.i1.a1', '288.j1.a1', '288.k1.a1', '288.k1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3277, -1, 7673, -1, 4545, -1, 7598, -1], 'generators': [348, 81, 40364311680], 'label': '1728.47489.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.g1.a1', 'projective_image': '576.8487', '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': '1.1'}
  • id: 115938036
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.b1.a2', '48.c1.a1', '48.h1.a1', '48.h2.a1'], 'contains': ['192.a1.a1', '288.l1.a1', '288.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7205, -1, 8219, -1, 2426, -1, 5797, -1], 'generators': [90801299, 348, 81], 'label': '1728.47489.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.h1.a1', 'projective_image': '576.8487', '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': '6.1'}
  • id: 115938037
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '32.b1.a1', '48.d1.a1'], 'contains': ['192.b1.a1', '288.l1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 5526, -1, 6762, -1, 4270, -1], 'generators': [90801299, 458, 168018480], 'label': '1728.47489.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '96.i1.a1', 'projective_image': '576.8487', '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': '6.1'}
  • id: 115938038
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.b1', '32.b1.a2', '48.d1.a1'], 'contains': ['192.b1.a1', '288.l1.a1', '288.n1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 4830, -1, 6762, -1, 4186, -1], 'generators': [6241985219, 458, 168018480], 'label': '1728.47489.96.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '96.i1.a2', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938039
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.c1', '32.b1.a1', '48.d1.b1'], 'contains': ['192.b1.b1', '288.l1.a1', '288.n1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 5349, -1, 6762, -1, 4662, -1], 'generators': [90801299, 458, 168018915], 'label': '1728.47489.96.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '96.i1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938040
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.d1', '32.b1.a2', '48.d1.b1'], 'contains': ['192.b1.b1', '288.l1.a1', '288.n1.b2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 4440, -1, 6762, -1, 4459, -1], 'generators': [6241985219, 458, 168018915], 'label': '1728.47489.96.i1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '96.i1.b2', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938041
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.e1', '32.b1.a1', '48.d1.c1'], 'contains': ['192.b1.c1', '288.l1.a1', '288.n1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 5475, -1, 6762, -1, 4120, -1], 'generators': [90801299, 134709555, 458], 'label': '1728.47489.96.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '96.i1.c1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938042
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.f1', '32.b1.a2', '48.d1.c1'], 'contains': ['192.b1.c1', '288.l1.a1', '288.n1.c2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4954, -1, 4582, -1, 6762, -1, 4055, -1], 'generators': [6241985219, 134709555, 458], 'label': '1728.47489.96.i1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '96.i1.c2', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.c2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938043
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.b1'], 'contains': ['18.c1.b1', '27.a1.a1', '36.t1.b1', '36.y1.c1', '36.y1.d1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4571, -1, 4260, -1, 6802, -1, 6095, -1], 'generators': [87091200, 40367945520, 20801370240, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.9.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '9.c1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938044
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '108.17', 'aut_weyl_index': 128, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '32.b1.a1', '48.e1.a1'], 'contains': ['192.c1.a1', '288.m1.a1', '288.n1.a1', '288.n1.b1', '288.n1.c1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5049, -1, 5433, -1, 6655, -1, 4369, -1], 'generators': [90801299, 348, 168018915], 'label': '1728.47489.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.j1.a1', 'projective_image': '1728.47489', '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': '18.4'}
  • id: 115938045
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '108.17', 'aut_weyl_index': 128, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.b1', '32.b1.a2', '48.e1.a1'], 'contains': ['192.c1.a1', '288.m1.a1', '288.n1.a2', '288.n1.b2', '288.n1.c2'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5049, -1, 4497, -1, 6655, -1, 4325, -1], 'generators': [6241985219, 348, 168018915], 'label': '1728.47489.96.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '96.j1.a2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 115938046
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 864, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '54.d1.a1'], 'contains': ['216.d1.a1', '216.e1.a1', '216.g1.a1', '216.m1.a1', '216.m1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9181, -1, 9233, -1, 871, -1, 9363, -1], 'generators': [7625520, 6314117040, 11335619, 13905647280], 'label': '1728.47489.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '108.a1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115938047
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.a1', '36.e1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.b1.b1', '216.c1.b1', '216.f1.a1', '216.h1.a1', '216.i1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3584, -1, 6968, -1, 4897, -1, 6836, -1], 'generators': [87091200, 40367945520, 20797746480, 6314117040], 'label': '1728.47489.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.b1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938048
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.d1.b1', '36.e1.b1', '54.a1.a1', '54.b1.b1', '54.c1.b1'], 'contains': ['216.b1.a1', '216.c1.a1', '216.f1.a1', '216.h1.a1', '216.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3584, -1, 7378, -1, 4897, -1, 6744, -1], 'generators': [40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.108.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.b1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938049
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.g1.a1', '36.h1.a1', '36.h1.b1', '54.a1.a1'], 'contains': ['216.c1.a1', '216.c1.b1', '216.d1.a1', '216.h1.a1', '216.i1.a1', '216.i1.b1', '216.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2588, -1, 4190, -1, 5592, -1, 6574, -1], 'generators': [40367945520, 7625520, 6314117040, 20757824640], 'label': '1728.47489.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '864.4709', '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: 115938050
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 432, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '54.b1.a1', '54.b1.b1', '54.d1.a1'], 'contains': ['216.e1.a1', '216.f1.a1', '216.k1.a1', '216.k1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6687, -1, 8309, -1, 1849, -1, 7719, -1], 'generators': [90801299, 7625520, 6314117040, 13941935280], 'label': '1728.47489.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938051
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.m1.a1', '54.c1.a1', '54.c1.b1', '54.d1.a1'], 'contains': ['216.f1.a1', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8254, -1, 8499, -1, 1399, -1, 7887, -1], 'generators': [7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '864.4709', '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: 115938052
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.n1.a1', '54.b1.b1', '54.c1.a1', '54.e1.a1'], 'contains': ['216.f1.a1', '216.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5771, -1, 7328, -1, 3681, -1, 7584, -1], 'generators': [7625520, 20765168579, 6314117040, 13941935280], 'label': '1728.47489.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938053
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.b1', '36.n1.b1', '54.b1.a1', '54.c1.b1', '54.e1.a1'], 'contains': ['216.f1.a1', '216.l1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5771, -1, 7818, -1, 3681, -1, 7777, -1], 'generators': [7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.108.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.f1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938054
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.c1'], 'contains': ['18.c1.c1', '27.a1.a1', '36.t1.c1', '36.y1.e1', '36.y1.f1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4571, -1, 4981, -1, 6802, -1, 5491, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 51610035, 6314117040, 11335619], 'label': '1728.47489.9.c1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '9.c1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.c1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938055
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 432, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '36.p1.a1', '36.q1.a1', '54.a1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.c1.b1', '216.d1.a1', '216.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6835, -1, 7933, -1, 3793, -1, 7182, -1], 'generators': [87091200, 40367945520, 7625520, 6314117040], 'label': '1728.47489.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.g1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938056
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 864, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.s1.a1', '36.t1.a1', '36.t1.b1', '36.t1.c1', '54.d1.a1'], 'contains': ['216.a1.a1', '216.e1.a1', '216.g1.a1', '216.n1.a1', '216.n1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9394, -1, 6507, -1, 1720, -1, 5167, -1], 'generators': [87091200, 7625520, 6314117040, 11335619], 'label': '1728.47489.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '108.h1.a1', 'projective_image': '864.4709', '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': '8.5'}
  • id: 115938057
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.v1.a1', '54.b1.b1'], 'contains': ['216.i1.a1', '216.k1.a1', '216.l1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4202, -1, 6924, -1, 3893, -1, 7131, -1], 'generators': [90801299, 20797746480, 6314117040, 13941935280], 'label': '1728.47489.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.i1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938058
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.b1', '36.v1.b1', '54.b1.a1'], 'contains': ['216.i1.b1', '216.k1.b1', '216.l1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4202, -1, 8014, -1, 3893, -1, 7668, -1], 'generators': [90801299, 13945559040, 6314117040, 20757824640], 'label': '1728.47489.108.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.i1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938059
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.a1', '36.x1.a1', '36.y1.a1', '36.y1.c1', '36.y1.e1', '54.b1.b1'], 'contains': ['216.b1.a1', '216.k1.a1', '216.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3931, -1, 3361, -1, 4056, -1, 6631, -1], 'generators': [90801299, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.j1.a1', 'projective_image': '864.4709', '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': '16.11'}
  • id: 115938060
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 864, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.b1', '36.x1.b1', '36.y1.b1', '36.y1.d1', '36.y1.f1', '54.b1.a1'], 'contains': ['216.b1.b1', '216.k1.b1', '216.l1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [3931, -1, 5066, -1, 4056, -1, 6790, -1], 'generators': [94435139, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.108.j1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.j1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938061
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.a1.a1', '72.e1.a1', '72.e1.b1', '72.h1.a1', '72.k1.a1', '72.m1.a1', '72.n1.a1'], 'contains': ['288.a1.a1', '288.f1.a1', '432.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7892, -1, 8909, -1, 2683, -1, 7699, -1], 'generators': [458, 7625520, 6314117040], 'label': '1728.47489.144.a1.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.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938062
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.b1.a1', '72.f1.a1', '72.f1.b1', '72.i1.a1', '72.l1.a1', '72.o1.a1', '72.p1.a1'], 'contains': ['288.b1.a1', '288.g1.a1', '432.a1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7629, -1, 9349, -1, 2555, -1, 8608, -1], 'generators': [348, 7625520, 6314117040], 'label': '1728.47489.144.b1.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.b1.a1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938063
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.g1.a1', '72.g1.b1', '72.g1.c1', '72.g1.d1', '72.j1.a1', '72.q1.a1', '72.r1.a1'], 'contains': ['288.c1.a1', '288.h1.a1', '432.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6381, -1, 5851, -1, 5012, -1, 6295, -1], 'generators': [7625520, 81, 6314117040], 'label': '1728.47489.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938064
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.e1.a1', '72.e1.b1', '72.h1.a1', '72.u1.a1', '72.x1.a1', '72.x1.b1', '72.ba1.a1'], 'contains': ['288.a1.a1', '288.i1.a1', '432.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4352, -1, 7542, -1, 4673, -1, 7074, -1], 'generators': [458, 40364311680, 6314117040], 'label': '1728.47489.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938065
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.g1.a1', '24.y1.a1', '24.y1.b1', '36.a1.a1', '36.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8855, -1, 9407, -1, 843, -1, 9692, -1], 'generators': [348, 7625520, 81, 6314117040, 11335619, 13905647280], 'label': '1728.47489.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115938066
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.f1.a1', '72.f1.b1', '72.i1.a1', '72.v1.a1', '72.y1.a1', '72.y1.b1', '72.bb1.a1'], 'contains': ['288.b1.a1', '288.j1.a1', '432.b1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3110, -1, 8166, -1, 4348, -1, 8390, -1], 'generators': [348, 40364311680, 6314117040], 'label': '1728.47489.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938067
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.g1.a1', '72.g1.c1', '72.j1.a1', '72.w1.a1', '72.z1.a1', '72.z1.b1', '72.bc1.a1'], 'contains': ['288.c1.a1', '288.k1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2306, -1, 4825, -1, 5561, -1, 6087, -1], 'generators': [81, 40364311680, 6314117040], 'label': '1728.47489.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '864.4709', '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: 115938068
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.g1.b1', '72.g1.d1', '72.j1.a1', '72.w1.b1', '72.z1.a1', '72.z1.b1', '72.bc1.b1'], 'contains': ['288.c1.a1', '288.k1.b1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2306, -1, 4678, -1, 5561, -1, 6153, -1], 'generators': [81, 6314117040, 40451402880], 'label': '1728.47489.144.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.f1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938069
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.d1.b1', '48.d1.c1', '72.k1.a1', '72.bf1.a1', '72.bf1.b1'], 'contains': ['288.a1.a1', '288.l1.a1', '432.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6265, -1, 6743, -1, 2957, -1, 6365, -1], 'generators': [90801299, 458, 6314117040], 'label': '1728.47489.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '144.g1.a1', 'projective_image': '288.1036', '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: 115938070
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.e1.a1', '72.l1.a1', '72.bg1.a1', '72.bg1.b1'], 'contains': ['288.b1.a1', '288.m1.a1', '432.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6146, -1, 8220, -1, 2859, -1, 7649, -1], 'generators': [90801299, 348, 6314117040], 'label': '1728.47489.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '144.h1.a1', 'projective_image': '864.4709', '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': '12.4'}
  • id: 115938071
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.y1.a1', '36.y1.b1', '48.d1.a1', '48.e1.a1'], 'contains': ['288.d1.a1', '288.n1.a1', '288.n1.a2', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4727, -1, 3819, -1, 7218, -1, 5023, -1], 'generators': [90801299, 6314117040, 168018480], 'label': '1728.47489.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '144.i1.a1', 'projective_image': '864.4709', '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': '6.1'}
  • id: 115938072
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.b1', '36.y1.c1', '36.y1.d1', '48.d1.b1', '48.e1.a1'], 'contains': ['288.d1.b1', '288.n1.b1', '288.n1.b2', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4727, -1, 3559, -1, 7218, -1, 5290, -1], 'generators': [90801299, 168018915, 6314117040], 'label': '1728.47489.144.i1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '144.i1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938073
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.c1', '36.y1.e1', '36.y1.f1', '48.d1.c1', '48.e1.a1'], 'contains': ['288.d1.c1', '288.n1.c1', '288.n1.c2', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4727, -1, 3713, -1, 7218, -1, 4988, -1], 'generators': [90801299, 134709555, 6314117040], 'label': '1728.47489.144.i1.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '144.i1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938074
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.c1.a1', '72.e1.a1', '72.m1.a1', '72.u1.a1', '72.x1.a1', '72.bf1.a1', '72.bh1.a1'], 'contains': ['288.a1.a1', '432.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4795, -1, 7154, -1, 4036, -1, 6906, -1], 'generators': [458, 40367945520, 6314117040], 'label': '1728.47489.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.j1.a1', 'projective_image': '288.1036', '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': '2.1'}
  • id: 115938075
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '72.c1.b1', '72.e1.b1', '72.m1.a1', '72.u1.a1', '72.x1.b1', '72.bf1.b1', '72.bh1.b1'], 'contains': ['288.a1.a1', '432.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4795, -1, 7729, -1, 4036, -1, 7329, -1], 'generators': [458, 20761458480, 6314117040], 'label': '1728.47489.144.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.j1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938076
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 216, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.b1.b1', '24.c1.b1', '24.f1.a1', '24.l1.a1', '24.m1.b1', '36.c1.a1', '36.d1.a1', '36.e1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3654, -1, 7986, -1, 4792, -1, 8191, -1], 'generators': [87091200, 40367945520, 348, 20797746480, 81, 6314117040], 'label': '1728.47489.12.b1.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': '12.b1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938077
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.d1.a1', '72.f1.a1', '72.o1.a1', '72.v1.a1', '72.y1.a1', '72.bg1.a1', '72.bi1.a1'], 'contains': ['288.b1.a1', '432.d1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3838, -1, 7583, -1, 3953, -1, 8126, -1], 'generators': [40367945520, 348, 6314117040], 'label': '1728.47489.144.k1.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': '144.k1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115938078
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '72.d1.b1', '72.f1.b1', '72.o1.a1', '72.v1.a1', '72.y1.b1', '72.bg1.b1', '72.bi1.b1'], 'contains': ['288.b1.a1', '432.d1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3838, -1, 8797, -1, 3953, -1, 8275, -1], 'generators': [348, 20761458480, 6314117040], 'label': '1728.47489.144.k1.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': '144.k1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938079
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.g1.a1', '72.g1.b1', '72.q1.a1', '72.w1.a1', '72.w1.b1', '72.z1.a1', '72.bj1.a1'], 'contains': ['288.c1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2855, -1, 5700, -1, 5354, -1, 6033, -1], 'generators': [40367945520, 81, 6314117040], 'label': '1728.47489.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.l1.a1', 'projective_image': '864.4709', '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: 115938080
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '72.g1.c1', '72.g1.d1', '72.q1.a1', '72.w1.a1', '72.w1.b1', '72.z1.b1', '72.bj1.b1'], 'contains': ['288.c1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2855, -1, 5752, -1, 5354, -1, 6232, -1], 'generators': [20761458480, 81, 6314117040], 'label': '1728.47489.144.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.l1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938081
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.h1.a1', '72.bm1.a1', '72.bm1.b1'], 'contains': ['288.f1.a1', '288.i1.a1', '432.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7744, -1, 9553, -1, 2284, -1, 8980, -1], 'generators': [87091200, 458, 40364311680], 'label': '1728.47489.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.m1.a1', 'projective_image': '576.8487', '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: 115938082
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.i1.a1', '72.bn1.a1', '72.bn1.b1'], 'contains': ['288.g1.a1', '288.j1.a1', '432.e1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7515, -1, 9904, -1, 2147, -1, 9147, -1], 'generators': [87091200, 348, 40364311680], 'label': '1728.47489.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.n1.a1', 'projective_image': '1728.47489', '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: 115938083
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.j1.a1'], 'contains': ['288.h1.a1', '288.k1.a1', '288.k1.b1', '432.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6496, -1, 6794, -1, 3650, -1, 6433, -1], 'generators': [87091200, 81, 40364311680], 'label': '1728.47489.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '144.o1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938084
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.k1.a1', '72.bm1.a1', '72.bm1.b1'], 'contains': ['288.f1.a1', '288.l1.a1', '432.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8898, -1, 9489, -1, 1286, -1, 9046, -1], 'generators': [6241985219, 458, 6310483200], 'label': '1728.47489.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.p1.a1', 'projective_image': '576.8487', '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: 115938085
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.p2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h2.a1', '72.k1.a1', '72.bo1.a1', '72.bo1.b1'], 'contains': ['288.f1.a1', '288.l1.a1', '432.f2.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8741, -1, 7462, -1, 1615, -1, 5863, -1], 'generators': [90801299, 458, 7625520], 'label': '1728.47489.144.p2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '144.p2.a1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938086
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.l1.a1', '72.bn1.a1', '72.bn1.b1'], 'contains': ['288.g1.a1', '288.m1.a1', '432.f1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8199, -1, 9789, -1, 1104, -1, 9096, -1], 'generators': [6241985219, 348, 6310483200], 'label': '1728.47489.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.q1.a1', 'projective_image': '1728.47489', '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: 115938087
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 216, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.f1.a1', '24.l1.a1', '24.m1.a1', '36.c1.b1', '36.d1.b1', '36.e1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3654, -1, 7759, -1, 4792, -1, 7997, -1], 'generators': [40367945520, 348, 20801370240, 7625520, 81, 6314117040], 'label': '1728.47489.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.b1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938088
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.q2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h2.a1', '72.l1.a1', '72.bp1.a1', '72.bp1.b1'], 'contains': ['288.g1.a1', '288.m1.a1', '432.f2.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8080, -1, 9085, -1, 1514, -1, 5994, -1], 'generators': [90801299, 348, 7625520], 'label': '1728.47489.144.q2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '144.q2.a1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115938089
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.n1.a1', '72.bm1.a1', '72.bo1.a1'], 'contains': ['288.f1.a1', '432.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9780, -1, 9307, -1, 1180, -1, 8728, -1], 'generators': [458, 7625520, 11335619], 'label': '1728.47489.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '144.r1.a1', 'projective_image': '576.8487', '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': '2.1'}
  • id: 115938090
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '72.n1.a1', '72.bm1.b1', '72.bo1.b1'], 'contains': ['288.f1.a1', '432.g1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9780, -1, 9432, -1, 1180, -1, 8836, -1], 'generators': [6321450899, 458, 7625520], 'label': '1728.47489.144.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '144.r1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938091
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.p1.a1', '72.bn1.a1', '72.bp1.a1'], 'contains': ['288.g1.a1', '432.g1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8994, -1, 9710, -1, 684, -1, 8880, -1], 'generators': [348, 7625520, 11335619], 'label': '1728.47489.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.s1.a1', 'projective_image': '1728.47489', '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: 115938092
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '72.p1.a1', '72.bn1.b1', '72.bp1.b1'], 'contains': ['288.g1.a1', '432.g1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8994, -1, 9744, -1, 684, -1, 8925, -1], 'generators': [6321450899, 348, 7625520], 'label': '1728.47489.144.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.s1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 115938093
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.k1.a1', '48.k1.b1', '48.k1.c1', '72.a1.a1', '72.bo1.a1', '72.bo1.b1'], 'contains': ['288.f1.a1', '432.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9523, -1, 6650, -1, 3412, -1, 4543, -1], 'generators': [87091200, 458, 7625520], 'label': '1728.47489.144.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.t1.a1', 'projective_image': '576.8487', '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': '6.1'}
  • id: 115938094
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.l1.a1', '48.m1.a1', '72.b1.a1', '72.bp1.a1', '72.bp1.b1'], 'contains': ['288.g1.a1', '432.h1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8562, -1, 8858, -1, 4142, -1, 4937, -1], 'generators': [87091200, 348, 7625520], 'label': '1728.47489.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.u1.a1', 'projective_image': '1728.47489', '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: 115938095
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.n1.a1', '48.n1.b1', '48.n1.c1', '72.r1.a1'], 'contains': ['288.h1.a1', '432.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7368, -1, 5600, -1, 5141, -1, 2901, -1], 'generators': [87091200, 7625520, 81], 'label': '1728.47489.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '1728.47489', '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': '3.1'}
  • id: 115938096
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.l1.a1', '48.n1.a1', '72.s1.a1', '72.bq1.a1', '72.bq1.b1'], 'contains': ['432.h1.a1', '576.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5357, -1, 6253, -1, 7114, -1, 3526, -1], 'generators': [87091200, 160796160, 7625520], 'label': '1728.47489.144.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '1728.47489', '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': '24.12'}
  • id: 115938097
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '48.l1.a1', '48.n1.b1', '72.s1.b1', '72.bq1.c1', '72.bq1.d1'], 'contains': ['432.h1.a1', '576.d1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5357, -1, 6003, -1, 7114, -1, 3865, -1], 'generators': [87091200, 160796595, 7625520], 'label': '1728.47489.144.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.w1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938098
    {'ambient': '1728.47489', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1536.408131703', 'aut_weyl_index': 9, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1', '6.f1.a1', '6.g1.a1', '9.a1.a1', '9.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6230, -1, 8074, -1, 3690, -1, 8389, -1], 'generators': [87091200, 40367945520, 348, 20801370240, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.3.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': '288.1036', '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': '96.160'}
  • id: 115938099
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 216, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.c1.a1', '24.c1.b1', '24.d1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.h1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2761, -1, 7102, -1, 5336, -1, 8094, -1], 'generators': [40367945520, 348, 7625520, 81, 6314117040, 20757824640], 'label': '1728.47489.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '288.1036', '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': '8.5'}
  • id: 115938100
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.c1', '48.l1.a1', '48.n1.c1', '72.s1.c1', '72.bq1.e1', '72.bq1.f1'], 'contains': ['432.h1.a1', '576.d1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5357, -1, 6155, -1, 7114, -1, 3476, -1], 'generators': [87091200, 7625520, 51610035], 'label': '1728.47489.144.w1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.w1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938101
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '48.m1.a1', '48.n1.a1', '48.n1.c1', '72.t1.a1'], 'contains': ['432.h1.a1', '576.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5296, -1, 4361, -1, 7544, -1, 2394, -1], 'generators': [87091200, 7625520, 160796430], 'label': '1728.47489.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.x1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115938102
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.c1', '48.m1.a1', '48.n1.a1', '48.n1.b1', '72.t1.b1'], 'contains': ['432.h1.a1', '576.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5296, -1, 5254, -1, 7544, -1, 2532, -1], 'generators': [160796241, 87091200, 7625520], 'label': '1728.47489.144.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.x1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938103
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.m1.a1', '48.n1.b1', '48.n1.c1', '72.t1.c1'], 'contains': ['432.h1.a1', '576.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5296, -1, 4320, -1, 7544, -1, 2604, -1], 'generators': [87091200, 7625520, 160796618], 'label': '1728.47489.144.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.x1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938104
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.p1.a1', '48.p1.b1', '48.p1.c1', '72.ba1.a1'], 'contains': ['288.i1.a1', '432.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1960, -1, 2480, -1, 8899, -1, 996, -1], 'generators': [458, 40364311680, 20757824640], 'label': '1728.47489.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.y1.a1', 'projective_image': '576.8487', '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': '3.1'}
  • id: 115938105
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.q1.a1', '48.r1.a1', '48.r1.a2', '72.bb1.a1'], 'contains': ['288.j1.a1', '432.i1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1469, -1, 1574, -1, 9192, -1, 930, -1], 'generators': [348, 40364311680, 20757824640], 'label': '1728.47489.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.z1.a1', 'projective_image': '1728.47489', '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': '3.1'}
  • id: 115938106
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.s1.a1', '48.s1.c1', '48.s1.e1', '72.bc1.a1'], 'contains': ['288.k1.a1', '432.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [969, -1, 1278, -1, 9027, -1, 655, -1], 'generators': [81, 40364311680, 20757824640], 'label': '1728.47489.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.ba1.a1', 'projective_image': '1728.47489', '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': '3.1'}
  • id: 115938107
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.s1.b1', '48.s1.d1', '48.s1.f1', '72.bc1.b1'], 'contains': ['288.k1.b1', '432.i1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [969, -1, 1328, -1, 9027, -1, 721, -1], 'generators': [20797746480, 81, 13905647280], 'label': '1728.47489.144.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.ba1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115938108
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.q1.a1', '48.s1.a1', '48.s1.b1', '72.bd1.a1'], 'contains': ['432.i1.a1', '576.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [479, -1, 1503, -1, 9502, -1, 568, -1], 'generators': [160796160, 40364311680, 20757824640], 'label': '1728.47489.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bb1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115938109
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.b1', '48.q1.a1', '48.s1.c1', '48.s1.d1', '72.bd1.b1'], 'contains': ['432.i1.a1', '576.d1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [479, -1, 994, -1, 9502, -1, 806, -1], 'generators': [160796595, 40364311680, 20757824640], 'label': '1728.47489.144.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bb1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938110
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.18491', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.d1.b1', '6.f1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.s1.a1', '24.s1.b1', '36.i1.a1', '36.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7062, -1, 8198, -1, 2173, -1, 8719, -1], 'generators': [90801299, 348, 7625520, 81, 6314117040, 13941935280], 'label': '1728.47489.12.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': '12.d1.a1', 'projective_image': '288.1036', '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': '48.43'}
  • id: 115938111
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.c1', '48.q1.a1', '48.s1.e1', '48.s1.f1', '72.bd1.c1'], 'contains': ['432.i1.a1', '576.d1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [479, -1, 1102, -1, 9502, -1, 771, -1], 'generators': [51610035, 40364311680, 20757824640], 'label': '1728.47489.144.bb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bb1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938112
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.b1', '48.r1.a1', '48.s1.a1', '48.s1.f1', '72.be1.a1'], 'contains': ['432.i1.a1', '576.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 748, -1, 9668, -1, 321, -1], 'generators': [25916970240, 32736493440, 160796430], 'label': '1728.47489.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.a1', 'projective_image': '1728.47489', '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': '12.3'}
  • id: 115938113
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.b1', '48.r1.a2', '48.s1.b1', '48.s1.e1', '72.be1.a2'], 'contains': ['432.i1.a1', '576.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 533, -1, 9668, -1, 356, -1], 'generators': [160796430, 40364311680, 20757824640], 'label': '1728.47489.144.bc1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.a2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938114
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.c1', '48.r1.a1', '48.s1.b1', '48.s1.c1', '72.be1.b1'], 'contains': ['432.i1.a1', '576.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 1239, -1, 9668, -1, 391, -1], 'generators': [160796241, 25916970240, 32736493440], 'label': '1728.47489.144.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938115
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.c1', '48.r1.a2', '48.s1.a1', '48.s1.d1', '72.be1.b2'], 'contains': ['432.i1.a1', '576.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 1066, -1, 9668, -1, 444, -1], 'generators': [160796241, 40364311680, 20757824640], 'label': '1728.47489.144.bc1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.b2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.b2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938116
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.r1.a1', '48.s1.d1', '48.s1.e1', '72.be1.c1'], 'contains': ['432.i1.a1', '576.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 562, -1, 9668, -1, 533, -1], 'generators': [25916970240, 32736493440, 160796618], 'label': '1728.47489.144.bc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938117
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.r1.a2', '48.s1.c1', '48.s1.f1', '72.be1.c2'], 'contains': ['432.i1.a1', '576.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 385, -1, 9668, -1, 498, -1], 'generators': [40364311680, 160796618, 20757824640], 'label': '1728.47489.144.bc1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '144.bc1.c2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.c2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115938118
    {'ambient': '1728.47489', 'aut_centralizer_order': 3456, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '2.a1.a1', 'complements': ['9.c1.b1', '9.c1.c1', '9.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.f1.a1', '96.g1.a1', '96.h1.a1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5828, 9327, 8102, 8263, 3986, 3033, 6905, 7332], 'generators': [348, 81], 'label': '1728.47489.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['576.a1.a1', '576.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '576.8487', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.204', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938119
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.p1.a1', '64.a1.a1', '96.b1.a1', '96.i1.a1', '96.i1.a2'], 'contains': ['576.a1.a1', '576.d1.a1', '576.e1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [895, -1, 4718, -1, 7408, -1, 3230, -1], 'generators': [458, 160796160], 'label': '1728.47489.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '576.8487', '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': '2.1'}
  • id: 115938120
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '48.p1.b1', '64.a1.a1', '96.b1.b1', '96.i1.b1', '96.i1.b2'], 'contains': ['576.a1.a1', '576.d1.b1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [895, -1, 4428, -1, 7408, -1, 3930, -1], 'generators': [458, 160796595], 'label': '1728.47489.192.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.b1.b1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938121
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.e1.b1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '36.k1.a1', '36.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8508, -1, 9065, -1, 1418, -1, 9312, -1], 'generators': [348, 7625520, 81, 6314117040, 11335619, 13941935280], 'label': '1728.47489.12.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': '12.e1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115938122
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.c1', '48.p1.c1', '64.a1.a1', '96.b1.c1', '96.i1.c1', '96.i1.c2'], 'contains': ['576.a1.a1', '576.d1.c1', '576.e1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [895, -1, 4630, -1, 7408, -1, 3128, -1], 'generators': [458, 51610035], 'label': '1728.47489.192.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.b1.c1', 'projective_image': '576.8487', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938123
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.q1.a1', '64.a1.a1', '96.c1.a1', '96.j1.a1', '96.j1.a2'], 'contains': ['576.b1.a1', '576.d1.a1', '576.d1.b1', '576.d1.c1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2175, -1, 4530, -1, 7331, -1, 3696, -1], 'generators': [348, 160796595], 'label': '1728.47489.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.c1.a1', 'projective_image': '1728.47489', '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': '2.1'}
  • id: 115938124
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1152, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.r1.a1', '48.r1.a2', '64.a1.a1', '96.d1.a1'], 'contains': ['576.b1.a1', '576.e1.a1', '576.e1.b1', '576.e1.c1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1242, -1, 595, -1, 7489, -1, 2262, -1], 'generators': [348, 160796618], 'label': '1728.47489.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '192.d1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938125
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.s1.a1', '48.s1.b1', '64.a1.a1', '96.e1.a1'], 'contains': ['576.c1.a1', '576.d1.a1', '576.e1.a1', '576.e1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [575, -1, 3146, -1, 7679, -1, 2320, -1], 'generators': [160796160, 81], 'label': '1728.47489.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '192.e1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938126
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.b1', '48.s1.c1', '48.s1.d1', '64.a1.a1', '96.e1.b1'], 'contains': ['576.c1.a1', '576.d1.b1', '576.e1.b1', '576.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [575, -1, 2057, -1, 7679, -1, 2630, -1], 'generators': [160796595, 81], 'label': '1728.47489.192.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '192.e1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938127
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.c1', '48.s1.e1', '48.s1.f1', '64.a1.a1', '96.e1.c1'], 'contains': ['576.c1.a1', '576.d1.c1', '576.e1.a1', '576.e1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [575, -1, 406, -1, 7679, -1, 2558, -1], 'generators': [81, 51610035], 'label': '1728.47489.192.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '192.e1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938128
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.r1.a1', '72.s1.a1', '72.s1.b1', '72.s1.c1', '72.t1.a1', '72.t1.b1', '72.t1.c1', '108.g1.a1', '108.h1.a1'], 'contains': ['432.a1.a1', '432.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8052, 4473, 5233, 2819, 4245, 5924, 3707, 4076], 'generators': [87091200, 7625520, 6314117040], 'label': '1728.47489.216.a1.a1', 'mobius_quo': 0, 'mobius_sub': -108, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['54.a1.a1', '72.a1.a1', '72.b1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938129
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '24.b1.b1', 'complements': ['8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.d1.a1', '72.bj1.a1', '72.bk1.a1', '72.bk1.c1', '72.bk1.e1', '72.bl1.a1', '72.bl1.c1', '72.bl1.e1', '108.b1.b1', '108.j1.a1'], 'contains': ['432.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3314, 2046, 2719, 3788, 5463, 7251, 4409, 3197], 'generators': [40367945520, 20801370240, 6314117040], 'label': '1728.47489.216.b1.a1', 'mobius_quo': 0, 'mobius_sub': -108, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['54.a1.a1', '72.c1.a1', '72.d1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938130
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '24.b1.a1', 'complements': ['8.d1.a1', '8.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.d1.b1', '72.bj1.b1', '72.bk1.b1', '72.bk1.d1', '72.bk1.f1', '72.bl1.b1', '72.bl1.d1', '72.bl1.f1', '108.b1.a1', '108.j1.b1'], 'contains': ['432.d1.b1'], 'core': '216.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3314, 2046, 4016, 4544, 5463, 7251, 4766, 4924], 'generators': [13945559040, 6314117040, 40443787440], 'label': '1728.47489.216.b1.b1', 'mobius_quo': 0, 'mobius_sub': -108, 'normal_closure': '216.b1.b1', 'normal_contained_in': ['54.a1.a1', '72.c1.b1', '72.d1.b1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.b1', 'projective_image': '864.4709', 'quotient_action_image': '24.12', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '216.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938131
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '72.g1.b1', '108.b1.b1', '108.c1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3639, -1, 7445, -1, 4446, -1, 6833, -1], 'generators': [40367945520, 7625520, 6314117040], 'label': '1728.47489.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115938132
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.f1.a1', '24.t1.a1', '36.l1.a1', '36.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6661, -1, 8380, -1, 2841, -1, 8572, -1], 'generators': [348, 7625520, 20765168579, 81, 6314117040, 13941935280], 'label': '1728.47489.12.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': '12.f1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115938133
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '72.f1.b1', '72.g1.c1', '72.g1.d1', '108.b1.a1', '108.c1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3639, -1, 7122, -1, 4446, -1, 6868, -1], 'generators': [87091200, 20797746480, 6314117040], 'label': '1728.47489.216.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '216.c1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938134
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.i1.a1', '72.j1.a1', '108.a1.a1', '108.c1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7134, -1, 8945, -1, 2786, -1, 8443, -1], 'generators': [87091200, 40364311680, 6314117040], 'label': '1728.47489.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '864.4709', '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': '8.3'}
  • id: 115938135
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.l1.a1', '108.a1.a1', '108.d1.a1', '108.h1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '432.f1.a1', '432.f2.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8283, -1, 8991, -1, 1720, -1, 8167, -1], 'generators': [90801299, 7625520, 6314117040], 'label': '1728.47489.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '216.e1.a1', 'projective_image': '864.4709', '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': '4.2'}
  • id: 115938136
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.o1.a1', '72.q1.a1', '108.b1.a1', '108.b1.b1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.f1.b1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6653, -1, 7752, -1, 3086, -1, 7397, -1], 'generators': [7625520, 6314117040, 13941935280], 'label': '1728.47489.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.f1.a1', 'projective_image': '864.4709', '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: 115938137
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '72.p1.a1', '108.a1.a1', '108.e1.a1', '108.h1.a1'], 'contains': ['432.a1.a1', '432.g1.a1', '432.g1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9267, -1, 9202, -1, 1414, -1, 8782, -1], 'generators': [7625520, 6314117040, 11335619], 'label': '1728.47489.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '216.g1.a1', 'projective_image': '864.4709', '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': '2.1'}
  • id: 115938138
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1.a1', '72.v1.a1', '72.w1.a1', '72.w1.b1', '108.b1.a1', '108.b1.b1', '108.c1.a1'], 'contains': ['432.b1.a1', '432.d1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2750, -1, 7060, -1, 4883, -1, 6747, -1], 'generators': [40367945520, 20797746480, 6314117040], 'label': '1728.47489.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '864.4709', '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: 115938139
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '24.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1.a1', '72.y1.a1', '72.z1.a1', '108.b1.b1', '108.c1.a1', '108.i1.a1'], 'contains': ['432.b1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3386, -1, 6935, -1, 4772, -1, 6798, -1], 'generators': [20797746480, 6314117040, 13941935280], 'label': '1728.47489.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.i1.a1', 'projective_image': '864.4709', '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': '8.3'}
  • id: 115938140
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1.b1', '72.y1.b1', '72.z1.b1', '108.b1.a1', '108.c1.a1', '108.i1.b1'], 'contains': ['432.b1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3386, -1, 7390, -1, 4772, -1, 6945, -1], 'generators': [20797746480, 6314117040, 40443787440], 'label': '1728.47489.216.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.i1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115938141
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 576, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '72.bc1.b1', '72.bd1.a1', '72.bd1.b1', '72.bd1.c1', '72.be1.a1', '72.be1.a2', '72.be1.b1', '72.be1.b2', '72.be1.c1', '72.be1.c2', '108.c1.a1'], 'contains': ['432.b1.a1', '432.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1877, -1, 2213, -1, 8796, -1, 1383, -1], 'generators': [40364311680, 6314117040, 20757824640], 'label': '1728.47489.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.j1.a1', 'projective_image': '864.4709', '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': '12.3'}
  • id: 115938142
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1.a1', '72.bg1.a1', '108.d1.a1', '108.i1.a1', '108.j1.a1'], 'contains': ['432.c1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5378, -1, 6826, -1, 3184, -1, 6980, -1], 'generators': [90801299, 6314117040, 13941935280], 'label': '1728.47489.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '216.k1.a1', 'projective_image': '864.4709', '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': '8.3'}
  • id: 115938143
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.b1', '6.g1.a1'], 'contains': ['24.f1.a1', '24.t1.b1', '36.l1.b1', '36.n1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6661, -1, 8540, -1, 2841, -1, 8865, -1], 'generators': [348, 7625520, 20805080339, 81, 6314117040, 13941935280], 'label': '1728.47489.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.f1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115938144
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1728, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1.b1', '72.bg1.b1', '108.d1.a1', '108.i1.b1', '108.j1.b1'], 'contains': ['432.c1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5378, -1, 8233, -1, 3184, -1, 7447, -1], 'generators': [90801299, 13945559040, 6314117040], 'label': '1728.47489.216.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.k1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115938145
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1.a1', '72.bi1.a1', '108.f1.a1', '108.i1.a1', '108.j1.a1'], 'contains': ['432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4110, -1, 7228, -1, 3877, -1, 7018, -1], 'generators': [40440078659, 6314117040, 13941935280], 'label': '1728.47489.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '216.l1.a1', 'projective_image': '864.4709', '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: 115938146
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '72.bh1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1.b1', '72.bi1.b1', '108.f1.b1', '108.i1.b1', '108.j1.b1'], 'contains': ['432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4110, -1, 7963, -1, 3877, -1, 7482, -1], 'generators': [40356979139, 13945559040, 6314117040], 'label': '1728.47489.216.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.l1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938147
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bm1.a1', '72.bn1.a1', '108.a1.a1'], 'contains': ['432.e1.a1', '432.f1.a1', '432.g1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9419, -1, 9553, -1, 954, -1, 9272, -1], 'generators': [7625520, 11335619, 13905647280], 'label': '1728.47489.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.m1.a1', 'projective_image': '1728.47489', '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: 115938148
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bm1.b1', '72.bn1.b1', '108.a1.a1'], 'contains': ['432.e1.a1', '432.f1.a1', '432.g1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9419, -1, 9579, -1, 954, -1, 9344, -1], 'generators': [6321450899, 7625520, 13905647280], 'label': '1728.47489.216.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.m1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938149
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.a1', '72.bp1.a1', '72.bq1.a1', '72.bq1.c1', '72.bq1.e1', '108.h1.a1'], 'contains': ['432.f2.a1', '432.g1.a1', '432.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9511, -1, 6488, -1, 2049, -1, 4731, -1], 'generators': [87091200, 7625520, 11335619], 'label': '1728.47489.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '216.n1.a1', 'projective_image': '1728.47489', '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: 115938150
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3456, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.b1', '72.bp1.b1', '72.bq1.b1', '72.bq1.d1', '72.bq1.f1', '108.h1.a1'], 'contains': ['432.f2.a1', '432.g1.b1', '432.h1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9511, -1, 6375, -1, 2049, -1, 4593, -1], 'generators': [87091200, 6321450899, 7625520], 'label': '1728.47489.216.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '216.n1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938151
    {'ambient': '1728.47489', 'aut_centralizer_order': 6912, 'aut_label': '288.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b1.c1', '144.a1.a1', '144.d1.a1', '144.g1.a1', '144.j1.a1', '144.j1.b1'], 'contains': ['576.a1.a1', '864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5673, 7413, 7157, 6847, 4059, 3946, 6330, 6728], 'generators': [458, 6314117040], 'label': '1728.47489.288.a1.a1', 'mobius_quo': 1, 'mobius_sub': -864, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '72.c1.a1', '72.c1.b1', '96.a1.a1'], 'normal_contains': ['576.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '1.1', 'quotient_action_kernel': '288.1036', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938152
    {'ambient': '1728.47489', 'aut_centralizer_order': 6912, 'aut_label': '288.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.c1.a1', '96.d1.a1', '144.b1.a1', '144.e1.a1', '144.h1.a1', '144.k1.a1', '144.k1.b1'], 'contains': ['576.b1.a1', '864.a1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4459, 5832, 8140, 5561, 4195, 5012, 7528, 5489], 'generators': [348, 6314117040], 'label': '1728.47489.288.b1.a1', 'mobius_quo': 1, 'mobius_sub': -96, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['72.b1.a1', '72.d1.a1', '72.d1.b1', '96.a1.a1'], 'normal_contains': ['576.b1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '864.4709', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.194', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938153
    {'ambient': '1728.47489', 'aut_centralizer_order': 3456, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.e1.a1', '96.e1.b1', '96.e1.c1', '144.c1.a1', '144.f1.a1', '144.f1.b1', '144.l1.a1', '144.l1.b1'], 'contains': ['576.c1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3655, -1, 4714, -1, 4679, -1, 5961, -1], 'generators': [81, 6314117040], 'label': '1728.47489.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '864.4709', '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': '1.1'}
  • id: 115938154
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 108, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.f1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7369, -1, 8916, -1, 3207, -1, 8287, -1], 'generators': [87091200, 40367945520, 348, 7625520, 81, 6314117040], 'label': '1728.47489.12.g1.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': '12.g1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938155
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.a1', '72.bd1.a1', '72.bk1.a1', '72.bk1.b1', '96.b1.a1', '96.c1.a1', '96.e1.a1', '144.i1.a1'], 'contains': ['576.d1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2097, -1, 3568, -1, 7607, -1, 3659, -1], 'generators': [160796160, 6314117040], 'label': '1728.47489.288.d1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '288.d1.a1', 'projective_image': '864.4709', '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: 115938156
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.b1', '72.bd1.b1', '72.bk1.c1', '72.bk1.d1', '96.b1.b1', '96.c1.a1', '96.e1.b1', '144.i1.b1'], 'contains': ['576.d1.b1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2097, -1, 3382, -1, 7607, -1, 3974, -1], 'generators': [160796595, 6314117040], 'label': '1728.47489.288.d1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '288.d1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938157
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.c1', '72.bd1.c1', '72.bk1.e1', '72.bk1.f1', '96.b1.c1', '96.c1.a1', '96.e1.c1', '144.i1.c1'], 'contains': ['576.d1.c1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2097, -1, 3463, -1, 7607, -1, 3624, -1], 'generators': [51610035, 6314117040], 'label': '1728.47489.288.d1.c1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '288.d1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938158
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '72.be1.a1', '72.be1.a2', '72.bl1.a1', '72.bl1.b1', '96.b1.b1', '96.d1.a1', '96.e1.a1', '96.e1.c1'], 'contains': ['576.e1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [855, -1, 839, -1, 8011, -1, 2413, -1], 'generators': [160796430, 6314117040], 'label': '1728.47489.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '288.e1.a1', 'projective_image': '864.4709', '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': '1.1'}
  • id: 115938159
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.b1', '72.be1.b1', '72.be1.b2', '72.bl1.c1', '72.bl1.d1', '96.b1.c1', '96.d1.a1', '96.e1.a1', '96.e1.b1'], 'contains': ['576.e1.b1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [855, -1, 3067, -1, 8011, -1, 2448, -1], 'generators': [160796241, 6314117040], 'label': '1728.47489.288.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '288.e1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938160
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.c1', '72.be1.c1', '72.be1.c2', '72.bl1.e1', '72.bl1.f1', '96.b1.a1', '96.d1.a1', '96.e1.b1', '96.e1.c1'], 'contains': ['576.e1.c1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [855, -1, 475, -1, 8011, -1, 2667, -1], 'generators': [6314117040, 160796618], 'label': '1728.47489.288.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '288.e1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938161
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '144.a1.a1', '144.m1.a1', '144.p1.a1', '144.p2.a1', '144.r1.a1', '144.r1.b1', '144.t1.a1'], 'contains': ['576.a1.a1', '864.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8476, -1, 9380, -1, 2219, -1, 8639, -1], 'generators': [458, 7625520], 'label': '1728.47489.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '288.f1.a1', 'projective_image': '576.8487', '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': '1.1'}
  • id: 115938162
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '144.b1.a1', '144.n1.a1', '144.q1.a1', '144.q2.a1', '144.s1.a1', '144.s1.b1', '144.u1.a1'], 'contains': ['576.b1.a1', '864.b1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7943, -1, 9651, -1, 2147, -1, 8674, -1], 'generators': [348, 7625520], 'label': '1728.47489.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '288.g1.a1', 'projective_image': '1728.47489', '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: 115938163
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '144.c1.a1', '144.o1.a1', '144.v1.a1'], 'contains': ['576.c1.a1', '864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6490, -1, 5983, -1, 4127, -1, 6295, -1], 'generators': [7625520, 81], 'label': '1728.47489.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '288.h1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938164
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.d1.a1', '144.m1.a1', '144.y1.a1'], 'contains': ['576.a1.a1', '864.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4398, -1, 7600, -1, 4533, -1, 7006, -1], 'generators': [458, 40364311680], 'label': '1728.47489.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '288.i1.a1', 'projective_image': '576.8487', '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': '1.1'}
  • id: 115938165
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.g1.a1', '24.z1.a1', '24.z1.b1', '36.r1.a1', '36.s1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9119, -1, 8832, -1, 1664, -1, 5884, -1], 'generators': [87091200, 348, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.h1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115938166
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.e1.a1', '144.n1.a1', '144.z1.a1'], 'contains': ['576.b1.a1', '864.c1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3715, -1, 8085, -1, 4420, -1, 7603, -1], 'generators': [348, 40364311680], 'label': '1728.47489.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '288.j1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938167
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.f1.a1', '144.o1.a1', '144.ba1.a1'], 'contains': ['576.c1.a1', '864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2281, -1, 6278, -1, 4747, -1, 5996, -1], 'generators': [81, 40364311680], 'label': '1728.47489.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '288.k1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938169
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.i1.a1', '96.i1.a2', '96.i1.b1', '96.i1.b2', '96.i1.c1', '96.i1.c2', '144.g1.a1', '144.p1.a1', '144.p2.a1'], 'contains': ['576.a1.a1', '864.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7440, -1, 5603, -1, 2761, -1, 4645, -1], 'generators': [90801299, 458], 'label': '1728.47489.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.k1.a1', 'old_label': '288.l1.a1', 'projective_image': '576.8487', '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': '1.1'}
  • id: 115938170
    {'ambient': '1728.47489', 'aut_centralizer_order': 96, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.j1.a1', '96.j1.a2', '144.h1.a1', '144.q1.a1', '144.q2.a1'], 'contains': ['576.b1.a1', '864.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6278, -1, 8324, -1, 2693, -1, 6066, -1], 'generators': [90801299, 348], 'label': '1728.47489.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '288.m1.a1', 'projective_image': '1728.47489', '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': '6.1'}
  • id: 115938171
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.a1', '96.i1.a1', '96.j1.a1', '144.i1.a1'], 'contains': ['576.d1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4808, -1, 6708, -1, 4329, -1], 'generators': [90801299, 168018480], 'label': '1728.47489.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '288.n1.a1', 'projective_image': '1728.47489', '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': '6.1'}
  • id: 115938172
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.b1', '96.i1.a2', '96.j1.a2', '144.i1.a1'], 'contains': ['576.d1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4588, -1, 6708, -1, 4256, -1], 'generators': [6241985219, 168018480], 'label': '1728.47489.288.n1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '288.n1.a2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938173
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.c1', '96.i1.b1', '96.j1.a1', '144.i1.b1'], 'contains': ['576.d1.b1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4741, -1, 6708, -1, 4680, -1], 'generators': [90801299, 168018915], 'label': '1728.47489.288.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '288.n1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938174
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.d1', '96.i1.b2', '96.j1.a2', '144.i1.b1'], 'contains': ['576.d1.b1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4369, -1, 6708, -1, 4480, -1], 'generators': [6241985219, 168018915], 'label': '1728.47489.288.n1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '288.n1.b2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938175
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.e1', '96.i1.c1', '96.j1.a1', '144.i1.c1'], 'contains': ['576.d1.c1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4781, -1, 6708, -1, 4188, -1], 'generators': [90801299, 134709555], 'label': '1728.47489.288.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '288.n1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938176
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.a1.a1'], 'contains': ['24.h1.a1', '24.ba1.a1', '24.ba1.b1', '36.r1.a1', '36.t1.a1', '48.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5632, -1, 6326, -1, 6651, -1, 3982, -1], 'generators': [87091200, 458, 160796160, 7625520, 6314117040, 11335619], 'label': '1728.47489.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '12.i1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938177
    {'ambient': '1728.47489', 'aut_centralizer_order': 8, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.f1', '96.i1.c2', '96.j1.a2', '144.i1.c1'], 'contains': ['576.d1.c1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5088, -1, 4535, -1, 6708, -1, 4120, -1], 'generators': [6241985219, 134709555], 'label': '1728.47489.288.n1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.c1', 'old_label': '288.n1.c2', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.c2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115938178
    {'ambient': '1728.47489', 'aut_centralizer_order': 2304, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '216.a1.a1', '216.c1.a1', '216.c1.b1', '216.d1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1'], 'contains': ['864.a1.a1', '864.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7583, -1, 8210, -1, 2834, -1, 7565, -1], 'generators': [7625520, 6314117040], 'label': '1728.47489.432.a1.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.a1.a1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938179
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '144.f1.b1', '216.c1.a1', '216.c1.b1', '216.d1.a1', '216.h1.a1', '216.i1.a1', '216.i1.b1', '216.j1.a1'], 'contains': ['864.a1.a1', '864.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3454, -1, 6614, -1, 4606, -1, 6795, -1], 'generators': [40364311680, 6314117040], 'label': '1728.47489.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '864.4709', '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': '2.1'}
  • id: 115938180
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '144.h1.a1', '144.i1.a1', '144.i1.b1', '144.i1.c1', '216.e1.a1', '216.k1.a1', '216.k1.b1'], 'contains': ['864.a1.a1', '864.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5746, -1, 6326, -1, 2957, -1, 6367, -1], 'generators': [90801299, 6314117040], 'label': '1728.47489.432.c1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '432.c1.a1', 'projective_image': '864.4709', '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: 115938181
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '144.k1.a1', '144.l1.a1', '216.b1.a1', '216.c1.a1', '216.f1.a1', '216.h1.a1', '216.i1.a1', '216.k1.a1', '216.l1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3874, -1, 7051, -1, 4263, -1, 6833, -1], 'generators': [40367945520, 6314117040], 'label': '1728.47489.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.d1.a1', 'projective_image': '864.4709', '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': '2.1'}
  • id: 115938182
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.b1', '144.k1.b1', '144.l1.b1', '216.b1.b1', '216.c1.b1', '216.f1.a1', '216.h1.a1', '216.i1.b1', '216.k1.b1', '216.l1.b1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3874, -1, 7394, -1, 4263, -1, 6868, -1], 'generators': [20761458480, 6314117040], 'label': '1728.47489.432.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.d1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938183
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1.a1', '144.n1.a1', '144.o1.a1', '216.d1.a1', '216.m1.a1', '216.m1.b1'], 'contains': ['864.b1.a1', '864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7358, -1, 9545, -1, 2292, -1, 8927, -1], 'generators': [87091200, 40364311680], 'label': '1728.47489.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '1728.47489', '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: 115938184
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.p1.a1', '144.q1.a1', '216.e1.a1', '216.m1.a1', '216.m1.b1'], 'contains': ['864.b1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8404, -1, 9501, -1, 1486, -1, 9046, -1], 'generators': [90801299, 6310483200], 'label': '1728.47489.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.f1.a1', 'projective_image': '1728.47489', '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: 115938185
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '432.f2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.p2.a1', '144.q2.a1', '216.e1.a1', '216.n1.a1', '216.n1.b1'], 'contains': ['864.b1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8213, -1, 8042, -1, 1886, -1, 6103, -1], 'generators': [90801299, 7625520], 'label': '1728.47489.432.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '432.f2.a1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938186
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.a1', '144.s1.a1', '216.g1.a1', '216.m1.a1', '216.n1.a1'], 'contains': ['864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9331, -1, 9277, -1, 1297, -1, 8738, -1], 'generators': [7625520, 11335619], 'label': '1728.47489.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '432.g1.a1', 'projective_image': '1728.47489', '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: 115938187
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1', '4.a1.a1'], 'contains': ['24.h1.b1', '24.ba1.c1', '24.ba1.d1', '36.r1.a1', '36.t1.b1', '48.d1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5632, -1, 4960, -1, 6651, -1, 4617, -1], 'generators': [87091200, 458, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '12.i1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938188
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.b1', '144.s1.b1', '216.g1.a1', '216.m1.b1', '216.n1.b1'], 'contains': ['864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9331, -1, 9450, -1, 1297, -1, 8810, -1], 'generators': [6321450899, 7625520], 'label': '1728.47489.432.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '432.g1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938189
    {'ambient': '1728.47489', 'aut_centralizer_order': 576, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1', '144.w1.b1', '144.w1.c1', '144.x1.a1', '144.x1.b1', '144.x1.c1', '216.a1.a1', '216.n1.a1', '216.n1.b1'], 'contains': ['864.b1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8046, -1, 6207, -1, 4336, -1, 3736, -1], 'generators': [87091200, 7625520], 'label': '1728.47489.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '432.h1.a1', 'projective_image': '1728.47489', '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': '6.1'}
  • id: 115938190
    {'ambient': '1728.47489', 'aut_centralizer_order': 288, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2304, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.ba1.b1', '144.bb1.a1', '144.bb1.b1', '144.bb1.c1', '144.bc1.a1', '144.bc1.a2', '144.bc1.b1', '144.bc1.b2', '144.bc1.c1', '144.bc1.c2', '216.j1.a1'], 'contains': ['864.c1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1877, -1, 980, -1, 9027, -1, 655, -1], 'generators': [40364311680, 20757824640], 'label': '1728.47489.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '432.i1.a1', 'projective_image': '1728.47489', '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': '3.1'}
  • id: 115938191
    {'ambient': '1728.47489', 'aut_centralizer_order': 6912, 'aut_label': '576.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '192.b1.c1', '288.a1.a1', '288.f1.a1', '288.i1.a1', '288.l1.a1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5829, 8010, 5603, 6847, 4059, 3519, 4697, 6728], 'generators': [458], 'label': '1728.47489.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['192.a1.a1', '288.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '576.8487', 'quotient_action_image': '1.1', 'quotient_action_kernel': '576.8487', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938192
    {'ambient': '1728.47489', 'aut_centralizer_order': 6912, 'aut_label': '576.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '2.a1.a1', 'complements': ['3.c1.b1', '3.c1.c1', '3.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.c1.a1', '192.d1.a1', '288.b1.a1', '288.g1.a1', '288.j1.a1', '288.m1.a1'], 'contains': ['1728.a1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4869, 7011, 8112, 6066, 4195, 4372, 6727, 5614], 'generators': [348], 'label': '1728.47489.576.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.b1.a1', 'normal_contained_in': ['192.a1.a1', '288.b1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.b1.a1', 'projective_image': '1728.47489', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.987', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938193
    {'ambient': '1728.47489', 'aut_centralizer_order': 3456, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.e1.a1', '192.e1.b1', '192.e1.c1', '288.c1.a1', '288.h1.a1', '288.k1.a1', '288.k1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3869, -1, 4684, -1, 4640, -1, 4592, -1], 'generators': [81], 'label': '1728.47489.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '576.c1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938194
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1.a1', '144.bb1.a1', '192.b1.a1', '192.c1.a1', '192.e1.a1', '288.d1.a1', '288.n1.a1', '288.n1.a2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2151, -1, 4630, -1, 7370, -1, 3659, -1], 'generators': [160796160], 'label': '1728.47489.576.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '576.d1.a1', 'projective_image': '1728.47489', '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: 115938195
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1.b1', '144.bb1.b1', '192.b1.b1', '192.c1.a1', '192.e1.b1', '288.d1.b1', '288.n1.b1', '288.n1.b2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2151, -1, 4394, -1, 7370, -1, 3930, -1], 'generators': [160796595], 'label': '1728.47489.576.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '576.d1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938196
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1.c1', '144.bb1.c1', '192.b1.c1', '192.c1.a1', '192.e1.c1', '288.d1.c1', '288.n1.c1', '288.n1.c2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2151, -1, 4531, -1, 7370, -1, 3624, -1], 'generators': [51610035], 'label': '1728.47489.576.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '576.d1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115938197
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.x1.a1', '144.bc1.a1', '144.bc1.a2', '192.b1.b1', '192.d1.a1', '192.e1.a1', '192.e1.c1', '288.e1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [836, -1, 618, -1, 7546, -1, 2368, -1], 'generators': [160796430], 'label': '1728.47489.576.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '576.e1.a1', 'projective_image': '1728.47489', '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': '1.1'}
  • id: 115938198
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1', '4.a1.a1'], 'contains': ['24.h1.c1', '24.ba1.e1', '24.ba1.f1', '36.r1.a1', '36.t1.c1', '48.d1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5632, -1, 6228, -1, 6651, -1, 3753, -1], 'generators': [87091200, 458, 7625520, 51610035, 6314117040, 11335619], 'label': '1728.47489.12.i1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.c1', 'old_label': '12.i1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938199
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.x1.b1', '144.bc1.b1', '144.bc1.b2', '192.b1.c1', '192.d1.a1', '192.e1.a1', '192.e1.b1', '288.e1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [836, -1, 3096, -1, 7546, -1, 2448, -1], 'generators': [160796241], 'label': '1728.47489.576.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '576.e1.b1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938200
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.x1.c1', '144.bc1.c1', '144.bc1.c2', '192.b1.a1', '192.d1.a1', '192.e1.b1', '192.e1.c1', '288.e1.c1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [836, -1, 561, -1, 7546, -1, 2601, -1], 'generators': [160796618], 'label': '1728.47489.576.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '576.e1.c1', 'projective_image': '1728.47489', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938201
    {'ambient': '1728.47489', 'aut_centralizer_order': 13824, 'aut_label': '864.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 13824, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '288.b1.a1', '288.c1.a1', '288.d1.a1', '288.d1.b1', '288.d1.c1', '288.e1.a1', '288.e1.b1', '288.e1.c1', '432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '432.d1.b1'], 'contains': ['1728.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3948, 5721, 4708, 4983, 4263, 5225, 4627, 5049], 'generators': [6314117040], 'label': '1728.47489.864.a1.a1', 'mobius_quo': -1, 'mobius_sub': 864, 'normal_closure': '864.a1.a1', 'normal_contained_in': ['216.a1.a1', '216.b1.a1', '216.b1.b1', '288.a1.a1', '288.b1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.a1.a1', 'projective_image': '864.4709', 'quotient_action_image': '1.1', 'quotient_action_kernel': '864.4709', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115938202
    {'ambient': '1728.47489', 'aut_centralizer_order': 2304, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 13824, 'centralizer': '6.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.f1.a1', '288.g1.a1', '288.h1.a1', '432.a1.a1', '432.e1.a1', '432.f1.a1', '432.f2.a1', '432.g1.a1', '432.g1.b1', '432.h1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7994, -1, 9277, -1, 2256, -1, 8639, -1], 'generators': [7625520], 'label': '1728.47489.864.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '864.b1.a1', 'projective_image': '1728.47489', '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: 115938203
    {'ambient': '1728.47489', 'aut_centralizer_order': 1152, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 13824, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.i1.a1', '288.j1.a1', '288.k1.a1', '288.k1.b1', '432.b1.a1', '432.e1.a1', '432.i1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3727, -1, 6469, -1, 4533, -1, 6447, -1], 'generators': [40364311680], 'label': '1728.47489.864.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '864.c1.a1', 'projective_image': '1728.47489', '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: 115938204
    {'ambient': '1728.47489', 'aut_centralizer_order': 192, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 13824, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.l1.a1', '288.m1.a1', '288.n1.a1', '288.n1.a2', '288.n1.b1', '288.n1.b2', '288.n1.c1', '288.n1.c2', '432.c1.a1', '432.f1.a1', '432.f2.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6278, -1, 4799, -1, 2761, -1, 4662, -1], 'generators': [90801299], 'label': '1728.47489.864.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.k1.a1', 'old_label': '864.d1.a1', 'projective_image': '1728.47489', '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: 115938205
    {'ambient': '1728.47489', '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.d1.b1', '576.d1.c1', '576.e1.a1', '576.e1.b1', '576.e1.c1', '864.a1.a1', '864.b1.a1', '864.c1.a1', '864.d1.a1'], 'contains': [], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3948, 7011, 4684, 6066, 4263, 4372, 4592, 5614], 'generators': [], 'label': '1728.47489.1728.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1728.a1.a1', 'normal_contained_in': ['576.a1.a1', '576.b1.a1', '864.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': '1728.47489', '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: 115938206
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '768.1089108', 'aut_weyl_index': 18, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.a1.a1', '9.c1.a1', '12.i1.a1', '12.m1.a1', '12.m1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4836, -1, 5056, -1, 6839, -1, 5689, -1], 'generators': [87091200, 458, 40367945520, 20801370240, 160796160, 7625520, 6314117040, 11335619], 'label': '1728.47489.3.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': '288.1036', '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': '96.227'}
  • id: 115938207
    {'ambient': '1728.47489', 'aut_centralizer_order': 4, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.a1.a1'], 'contains': ['24.i1.a1', '24.bb1.a1', '24.bb1.b1', '36.s1.a1', '36.t1.a1', '36.t1.b1', '36.t1.c1', '48.e1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5935, -1, 5849, -1, 6509, -1, 4203, -1], 'generators': [87091200, 348, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '864.4709', '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': '72.43'}
  • id: 115938208
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1'], 'contains': ['24.m1.a1', '24.s1.a1', '24.t1.a1', '36.u1.a1', '36.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4372, -1, 7295, -1, 4135, -1, 7910, -1], 'generators': [90801299, 348, 20797746480, 81, 6314117040, 13941935280], 'label': '1728.47489.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.k1.a1', 'projective_image': '288.1036', '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': '48.43'}
  • id: 115938209
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.m1.b1', '24.s1.b1', '24.t1.b1', '36.u1.b1', '36.v1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4372, -1, 8259, -1, 4135, -1, 8379, -1], 'generators': [90801299, 348, 81, 13945559040, 6314117040, 20757824640], 'label': '1728.47489.12.k1.b1', '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.k1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115938210
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.b1'], 'contains': ['24.b1.a1', '24.s1.a1', '24.t1.a1', '36.w1.a1', '36.x1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4167, -1, 3937, -1, 4292, -1, 6866, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 81, 6314117040], 'label': '1728.47489.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.l1.a1', 'projective_image': '288.1036', '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': '48.43'}
  • id: 115938211
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.d1.a1'], 'contains': ['24.b1.b1', '24.s1.b1', '24.t1.b1', '36.w1.b1', '36.x1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4167, -1, 5743, -1, 4292, -1, 7311, -1], 'generators': [94435139, 348, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.12.l1.b1', '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.l1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115938212
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.b1.a1'], 'contains': ['24.u1.a1', '36.w1.a1', '36.y1.a1', '48.d1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 3259, -1, 7116, -1, 5570, -1], 'generators': [90801299, 458, 40367945520, 20801370240, 6314117040, 168018480], 'label': '1728.47489.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.a1', 'old_label': '12.m1.a1', 'projective_image': '288.1036', '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': '24.12'}
  • id: 115938213
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.b1.b1'], 'contains': ['24.u1.b1', '36.w1.b1', '36.y1.b1', '48.d1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 4623, -1, 7116, -1, 5792, -1], 'generators': [458, 94435139, 160796160, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.b1', 'old_label': '12.m1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938214
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1', '4.b1.a1'], 'contains': ['24.u1.c1', '36.w1.a1', '36.y1.c1', '48.d1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 2991, -1, 7116, -1, 6172, -1], 'generators': [90801299, 458, 40367945520, 20801370240, 168018915, 6314117040], 'label': '1728.47489.12.m1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.c1', 'old_label': '12.m1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938215
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.b1', '4.b1.b1'], 'contains': ['24.u1.d1', '36.w1.b1', '36.y1.d1', '48.d1.b1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 3796, -1, 7116, -1, 6292, -1], 'generators': [458, 94435139, 160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.12.m1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.d1', 'old_label': '12.m1.d1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938216
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1', '4.b1.a1'], 'contains': ['24.u1.e1', '36.w1.a1', '36.y1.e1', '48.d1.c1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 3425, -1, 7116, -1, 5413, -1], 'generators': [90801299, 134709555, 458, 40367945520, 20801370240, 6314117040], 'label': '1728.47489.12.m1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.e1', 'old_label': '12.m1.e1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938217
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '768.1089108', 'aut_weyl_index': 18, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '9.a1.a1', '9.c1.b1', '12.i1.b1', '12.m1.c1', '12.m1.d1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4836, -1, 4228, -1, 6839, -1, 6051, -1], 'generators': [87091200, 458, 40367945520, 20801370240, 160796595, 7625520, 6314117040, 11335619], 'label': '1728.47489.3.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.b1', 'old_label': '3.c1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938218
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.c1', '4.b1.b1'], 'contains': ['24.u1.f1', '36.w1.b1', '36.y1.f1', '48.d1.c1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3822, -1, 4276, -1, 7116, -1, 5690, -1], 'generators': [458, 94435139, 51610035, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.12.m1.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.f1', 'old_label': '12.m1.f1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938219
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.b1.a1'], 'contains': ['24.v1.a1', '36.x1.a1', '36.y1.a1', '36.y1.c1', '36.y1.e1', '48.e1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3448, -1, 3104, -1, 6902, -1, 5982, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 168018915, 6314117040], 'label': '1728.47489.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '864.4709', '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': '72.43'}
  • id: 115938220
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 16, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.b1.b1'], 'contains': ['24.v1.b1', '36.x1.b1', '36.y1.b1', '36.y1.d1', '36.y1.f1', '48.e1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3448, -1, 4177, -1, 6902, -1, 6081, -1], 'generators': [94435139, 348, 160796595, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.12.n1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '12.n1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 115938221
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '432.545', 'aut_weyl_index': 32, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.a2', '48.c1.a1', '48.d1.a1', '48.d1.b1', '48.d1.c1', '48.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4814, -1, 3842, -1, 6747, -1, 5066, -1], 'generators': [90801299, 348, 168018915, 81, 6314117040], 'label': '1728.47489.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 115938222
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.k1.b1', '48.k1.c1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.n1.b1', '48.n1.c1', '64.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5479, -1, 5897, -1, 6971, -1, 2517, -1], 'generators': [87091200, 348, 160796595, 7625520, 81], 'label': '1728.47489.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '576.8487', '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': '24.12'}
  • id: 115938223
    {'ambient': '1728.47489', 'aut_centralizer_order': 6, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['48.o1.a1', '48.p1.a1', '48.p1.b1', '48.p1.c1', '48.q1.a1', '48.r1.a1', '48.r1.a2', '48.s1.a1', '48.s1.b1', '48.s1.c1', '48.s1.d1', '48.s1.e1', '48.s1.f1', '64.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [747, -1, 1220, -1, 9562, -1, 486, -1], 'generators': [348, 160796595, 81, 40364311680, 20757824640], 'label': '1728.47489.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.c1.a1', 'projective_image': '576.8487', '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': '12.3'}
  • id: 115938224
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': ['96.j1.a1', '96.j1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.c1.b1', '36.f1.a1', '36.o1.a1', '54.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4040, 5360, 5116, 5253, 5147, 5438, 6758, 5065], 'generators': [87091200, 458, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.b1', '6.b1.a1', '6.b1.c1'], 'normal_contains': ['54.a1.a1', '72.a1.a1', '72.c1.a1', '72.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938225
    {'ambient': '1728.47489', 'aut_centralizer_order': 36, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': ['96.i1.b1', '96.i1.b2', '96.i1.c1', '96.i1.c2', '96.i1.a1', '96.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.h1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.d1.b1', '36.g1.a1', '36.p1.a1', '54.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3240, 2753, 6878, 3723, 4969, 7666, 8465, 3590], 'generators': [87091200, 40367945520, 348, 20801370240, 7625520, 6314117040], 'label': '1728.47489.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1', '6.c1.a1'], 'normal_contains': ['54.a1.a1', '72.b1.a1', '72.d1.a1', '72.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '864.4709', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938226
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['96.h1.a1', '96.i1.c1', '96.i1.c2', '96.i1.b1', '96.i1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.i1.a1', '9.c1.a1'], 'contains': ['54.a1.a1', '72.s1.a1', '72.bd1.a1', '72.bk1.a1', '72.bk1.b1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2219, 673, 4304, 680, 7574, 9443, 3545, 1534], 'generators': [87091200, 40367945520, 20801370240, 160796160, 7625520, 6314117040], 'label': '1728.47489.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '864.4709', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938227
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['96.h1.a1', '96.i1.c1', '96.i1.c2', '96.i1.a1', '96.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.c1.a1', '6.i1.b1', '9.c1.b1'], 'contains': ['54.a1.a1', '72.s1.b1', '72.bd1.b1', '72.bk1.c1', '72.bk1.d1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2219, 673, 3322, 1591, 7574, 9443, 4689, 655], 'generators': [87091200, 40367945520, 20801370240, 160796595, 7625520, 6314117040], 'label': '1728.47489.18.c1.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.b1', 'normal_contained_in': ['6.b1.b1', '6.c1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '864.4709', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938228
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '768.1089108', 'aut_weyl_index': 18, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '9.a1.a1', '9.c1.c1', '12.i1.c1', '12.m1.e1', '12.m1.f1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4836, -1, 4593, -1, 6839, -1, 5491, -1], 'generators': [87091200, 458, 40367945520, 20801370240, 7625520, 51610035, 6314117040, 11335619], 'label': '1728.47489.3.c1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.c1', 'old_label': '3.c1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.c1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938229
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': ['96.h1.a1', '96.i1.b1', '96.i1.b2', '96.i1.a1', '96.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '6.c1.a1', '6.i1.c1', '9.c1.c1'], 'contains': ['54.a1.a1', '72.s1.c1', '72.bd1.c1', '72.bk1.e1', '72.bk1.f1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2219, 673, 3958, 2502, 7574, 9443, 3461, 2413], 'generators': [87091200, 40367945520, 20801370240, 7625520, 51610035, 6314117040], 'label': '1728.47489.18.c1.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.c1', 'normal_contained_in': ['6.b1.c1', '6.c1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.c1', 'projective_image': '864.4709', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.c1.c1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 115938230
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.i1.a1', '36.l1.b1', '36.u1.b1', '36.w1.b1', '54.b1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4600, -1, 7607, -1, 3966, -1, 7397, -1], 'generators': [458, 7625520, 20805080339, 6314117040, 20757824640, 13941935280], 'label': '1728.47489.18.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': '288.1036', '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': '32.27'}
  • id: 115938231
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 216, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '9.a1.a1'], 'contains': ['36.c1.b1', '36.i1.a1', '36.l1.a1', '36.u1.a1', '36.w1.a1', '54.b1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4600, -1, 7188, -1, 3966, -1, 7122, -1], 'generators': [90801299, 458, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.18.d1.b1', '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.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 115938232
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.j1.a1', '36.n1.b1', '36.v1.b1', '36.x1.b1', '54.b1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4191, -1, 8279, -1, 3833, -1, 8781, -1], 'generators': [348, 7625520, 20805080339, 6314117040, 20757824640, 13941935280], 'label': '1728.47489.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '864.4709', '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': '96.160'}
  • id: 115938233
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 72, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '9.b1.a1'], 'contains': ['36.d1.b1', '36.j1.a1', '36.n1.a1', '36.v1.a1', '36.x1.a1', '54.b1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4191, -1, 7914, -1, 3833, -1, 8656, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 7625520, 6314117040], 'label': '1728.47489.18.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.e1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.b1', 'subgroup_fusion': None, 'weyl_group': '96.160'}
  • id: 115938234
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 216, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.k1.a1', '36.l1.a1', '54.c1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6450, -1, 7684, -1, 3415, -1, 7589, -1], 'generators': [458, 7625520, 6314117040, 11335619, 20757824640, 13941935280], 'label': '1728.47489.18.f1.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.f1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115938235
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 216, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '9.a1.a1'], 'contains': ['36.c1.b1', '36.k1.a1', '36.l1.b1', '54.c1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6450, -1, 7987, -1, 3415, -1, 7798, -1], 'generators': [458, 40367945520, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.18.f1.b1', '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.f1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 115938236
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '144.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.m1.a1', '36.n1.a1', '54.c1.a1'], 'core': '72.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6250, -1, 8416, -1, 2634, -1, 9045, -1], 'generators': [348, 7625520, 6314117040, 11335619, 20757824640, 13941935280], 'label': '1728.47489.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115938237
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 72, 'centralizer': '144.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '9.b1.a1'], 'contains': ['36.d1.b1', '36.m1.a1', '36.n1.b1', '54.c1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6250, -1, 8514, -1, 2634, -1, 9221, -1], 'generators': [40367945520, 348, 20801370240, 7625520, 6314117040, 11335619], 'label': '1728.47489.18.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 115938238
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 108, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.i1.a1', '36.k1.a1', '36.o1.a1', '36.r1.a1', '54.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8465, -1, 8104, -1, 2007, -1, 7693, -1], 'generators': [87091200, 458, 7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.18.h1.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.h1.a1', 'projective_image': '288.1036', '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': '16.11'}
  • id: 115938239
    {'ambient': '1728.47489', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1728.46116', 'aut_weyl_index': 8, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '12.h1.a1', '12.i1.a1', '12.i1.b1', '12.i1.c1', '12.j1.a1', '16.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5654, -1, 5841, -1, 6583, -1, 4019, -1], 'generators': [87091200, 348, 160796595, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 115938240
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.18491', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.j1.a1', '36.m1.a1', '36.p1.a1', '36.s1.a1', '54.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8256, -1, 9150, -1, 1844, -1, 9133, -1], 'generators': [87091200, 348, 7625520, 6314117040, 11335619, 13941935280], 'label': '1728.47489.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.i1.a1', 'projective_image': '864.4709', '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': '48.43'}
  • id: 115938241
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 108, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.l1.a1', '36.l1.b1', '36.o1.a1', '54.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6913, -1, 7862, -1, 3612, -1, 7488, -1], 'generators': [87091200, 458, 7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.18.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': '288.1036', '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': '32.27'}
  • id: 115938242
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.12882', 'aut_weyl_index': 36, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.b1.a1'], 'contains': ['36.n1.a1', '36.n1.b1', '36.p1.a1', '54.e1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6770, -1, 8576, -1, 3034, -1, 8963, -1], 'generators': [87091200, 348, 7625520, 20805080339, 6314117040, 13941935280], 'label': '1728.47489.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.k1.a1', 'projective_image': '864.4709', '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': '96.160'}
  • id: 115938243
    {'ambient': '1728.47489', 'aut_centralizer_order': 18, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.i1.a1', '6.i1.b1', '6.i1.c1'], 'contains': ['36.e1.a1', '36.e1.b1', '36.h1.a1', '36.h1.b1', '36.q1.a1', '54.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2634, -1, 4127, -1, 5861, -1, 5317, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 81, 6314117040], 'label': '1728.47489.18.l1.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': '18.l1.a1', 'projective_image': '864.4709', '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': '48.50'}
  • id: 115938244
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.h1.a1', '6.i1.a1', '6.i1.c1'], 'contains': ['54.a1.a1', '72.t1.a1', '72.be1.a1', '72.be1.a2', '72.bl1.a1', '72.bl1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2124, -1, 2535, -1, 8077, -1, 1974, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 160796430, 6314117040], 'label': '1728.47489.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.m1.a1', 'projective_image': '864.4709', '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': '48.50'}
  • id: 115938245
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '6.h1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['54.a1.a1', '72.t1.b1', '72.be1.b1', '72.be1.b2', '72.bl1.c1', '72.bl1.d1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2124, -1, 2859, -1, 8077, -1, 2028, -1], 'generators': [160796241, 87091200, 40367945520, 20801370240, 7625520, 6314117040], 'label': '1728.47489.18.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.m1.b1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.b1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 115938246
    {'ambient': '1728.47489', 'aut_centralizer_order': 12, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.955', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.i1.b1', '6.i1.c1'], 'contains': ['54.a1.a1', '72.t1.c1', '72.be1.c1', '72.be1.c2', '72.bl1.e1', '72.bl1.f1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2124, -1, 951, -1, 8077, -1, 2271, -1], 'generators': [87091200, 40367945520, 20801370240, 7625520, 6314117040, 160796618], 'label': '1728.47489.18.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.m1.c1', 'projective_image': '864.4709', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.c1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 115938247
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '72.a1.a1', '72.b1.a1', '72.r1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8745, 9244, 9150, 5651, 3068, 1517, 5200, 7662], 'generators': [87091200, 348, 7625520, 81, 6314117040], 'label': '1728.47489.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938248
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '24.b1.b1', 'complements': ['72.bq1.c1', '72.bq1.d1', '72.bq1.e1', '72.bq1.f1', '72.bq1.a1', '72.bq1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.b1', '12.l1.a1'], 'contains': ['48.f1.a1', '72.c1.a1', '72.d1.a1', '72.bj1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3454, 7011, 3759, 7245, 5854, 3389, 6366, 6422], 'generators': [40367945520, 348, 20801370240, 81, 6314117040], 'label': '1728.47489.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['72.c1.a1', '72.d1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938249
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': ['72.bq1.c1', '72.bq1.d1', '72.bq1.e1', '72.bq1.f1', '72.bq1.a1', '72.bq1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.b1.a1', '12.l1.b1'], 'contains': ['48.f1.b1', '72.c1.b1', '72.d1.b1', '72.bj1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3454, 7011, 5265, 9320, 5854, 3389, 6551, 8902], 'generators': [348, 81, 13945559040, 6314117040, 40443787440], 'label': '1728.47489.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['72.c1.b1', '72.d1.b1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '288.1036', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938250
    {'ambient': '1728.47489', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1728.46116', 'aut_weyl_index': 8, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.a1', '12.l1.a1', '12.m1.a1', '12.m1.c1', '12.m1.e1', '12.n1.a1', '16.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4099, -1, 3256, -1, 6983, -1, 5621, -1], 'generators': [90801299, 40367945520, 348, 20801370240, 168018915, 81, 6314117040], 'label': '1728.47489.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '288.1036', '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': '72.43'}
  • id: 115938251
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 864, 'centralizer': '24.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.c1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.f1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '72.g1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3715, -1, 7775, -1, 4588, -1, 8287, -1], 'generators': [40367945520, 348, 7625520, 81, 6314117040], 'label': '1728.47489.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '288.1036', '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': '4.2'}
  • id: 115938252
    {'ambient': '1728.47489', 'aut_centralizer_order': 72, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 864, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.f1.b1', '72.e1.b1', '72.f1.b1', '72.g1.c1', '72.g1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3715, -1, 8781, -1, 4588, -1, 8440, -1], 'generators': [87091200, 348, 20797746480, 81, 6314117040], 'label': '1728.47489.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 115938253
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.g1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 9360, -1, 2312, -1, 9409, -1], 'generators': [87091200, 348, 81, 40364311680, 6314117040], 'label': '1728.47489.24.d1.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': '24.d1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 115938254
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.h1.a1', '48.h2.a1', '72.k1.a1', '72.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8107, -1, 9081, -1, 1008, -1, 9320, -1], 'generators': [90801299, 348, 7625520, 81, 6314117040], 'label': '1728.47489.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.e1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 115938255
    {'ambient': '1728.47489', 'aut_centralizer_order': 144, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 432, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.b1.b1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.f1.b1', '72.m1.a1', '72.o1.a1', '72.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7133, -1, 8955, -1, 2463, -1, 8724, -1], 'generators': [348, 7625520, 81, 6314117040, 13941935280], 'label': '1728.47489.24.f1.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': '24.f1.a1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 115938256
    {'ambient': '1728.47489', 'aut_centralizer_order': 48, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 288, 'centralizer': '72.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.e1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.i1.a1', '48.i1.b1', '72.n1.a1', '72.p1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9226, -1, 9542, -1, 542, -1, 9655, -1], 'generators': [348, 7625520, 81, 6314117040, 11335619], 'label': '1728.47489.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.g1.a1', 'projective_image': '288.1036', '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: 115938257
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.a1.a1', '12.i1.a1'], 'contains': ['48.k1.a1', '72.a1.a1', '72.s1.a1', '72.t1.c1', '96.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5270, -1, 5118, -1, 7356, -1, 3114, -1], 'generators': [87091200, 458, 160796160, 7625520, 6314117040], 'label': '1728.47489.24.h1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '288.1036', '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': '24.12'}
  • id: 115938258
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.a1.a1', '12.i1.b1'], 'contains': ['48.k1.b1', '72.a1.a1', '72.s1.b1', '72.t1.a1', '96.b1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5270, -1, 4848, -1, 7356, -1, 4077, -1], 'generators': [87091200, 458, 160796595, 7625520, 6314117040], 'label': '1728.47489.24.h1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.h1.b1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938259
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 288, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.a1.a1', '12.i1.c1'], 'contains': ['48.k1.c1', '72.a1.a1', '72.s1.c1', '72.t1.b1', '96.b1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5270, -1, 5168, -1, 7356, -1, 3048, -1], 'generators': [87091200, 458, 7625520, 51610035, 6314117040], 'label': '1728.47489.24.h1.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.h1.c1', 'projective_image': '288.1036', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 115938260
    {'ambient': '1728.47489', 'aut_centralizer_order': 24, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.a1.a1', '12.j1.a1'], 'contains': ['48.l1.a1', '72.b1.a1', '72.s1.a1', '72.s1.b1', '72.s1.c1', '96.c1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5851, -1, 5067, -1, 7228, -1, 3718, -1], 'generators': [87091200, 348, 160796595, 7625520, 6314117040], 'label': '1728.47489.24.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '864.4709', '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': '24.12'}