Abstract group data - 288.630

Formats: - HTML - YAML - JSON - 2025-10-29T11:10:27.239471

• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 4, 6, 6, 6, 12, 4], 'aut_gens': [[1, 2, 8, 96], [53, 82, 136, 96], [1, 173, 183, 64], [1, 38, 284, 96], [53, 22, 188, 96], [1, 38, 104, 96], [53, 265, 227, 64], [49, 73, 231, 32]], 'aut_group': None, 'aut_hash': 696738818174563068, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 28, 'aut_perms': [188500223675288403348489771889, 33130079021035561206084284732, 218281745832664730541060658548, 166821325856134828727309356255, 185674207546471024996188979776, 68273763895804721725706901114, 63369509941632336963354104893], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [3, 2, 2, 1], [3, 4, 1, 1], [4, 12, 2, 2], [4, 18, 2, 2], [6, 2, 2, 3], [6, 4, 1, 3], [6, 4, 4, 2], [12, 12, 4, 2]], 'aut_supersolvable': False, 'aut_tex': 'D_6^2.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '72.40', 'autcentquo_hash': 40, 'autcentquo_nilpotent': False, 'autcentquo_order': 72, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 2, 2], [3, 4, 1], [4, 12, 4], [4, 18, 4], [6, 2, 6], [6, 4, 11], [12, 12, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '72.46', 'commutator_count': 2, 'commutator_label': '36.14', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 630, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 12, 1, 4], [4, 18, 1, 2], [4, 18, 2, 1], [6, 2, 1, 6], [6, 4, 1, 11], [12, 12, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 12, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '72.46', 'hash': 630, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 6, 3], 'inner_gens': [[1, 54, 60, 96], [53, 2, 88, 96], [53, 18, 8, 192], [1, 2, 200, 96]], 'inner_hash': 46, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': False, 'inner_tex': 'S_3\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 22], [4, 12]], 'label': '288.630', 'linC_count': 264, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 16, 'linQ_dim': 8, 'linQ_dim_count': 6, 'linR_count': 94, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:Q8', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 42, 'number_divisions': 37, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 100, 'number_subgroup_classes': 175, 'number_subgroups': 594, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 8], [4, 120], [6, 56], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[49, 6, 8, 96], [1, 54, 40, 192], [1, 50, 8, 192], [53, 2, 8, 192], [49, 77, 147, 32]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [806400, 367936, 368040, 368047, 368058], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 17]], 'representations': {'PC': {'code': 821659005897799949323590479107, 'gens': [1, 2, 4, 7], 'pres': [7, -2, -2, -2, 2, -2, -3, -3, 757, 36, 1683, 1242, 80, 1411, 102, 1356, 1203]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1177625, 793169, 1182397, 47305, 737409, 1675603, 78193]}, 'Perm': {'d': 18, 'gens': [358477182166446, 359791126421881, 136095256, 136095240, 7, 776764801612800, 1129924059264000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:Q_8', '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: 103725725
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 630, 'group_order': 288, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 103725736
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 630, 'group_order': 288, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 52, 'size': 1}
  • id: 103725747
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 630, 'group_order': 288, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 48, 'size': 1}
  • id: 103725758
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 630, 'group_order': 288, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 4, 'size': 1}
  • id: 103725762
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 630, 'group_order': 288, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 2}
  • id: 103725763
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 630, 'group_order': 288, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 49, 'size': 2}
  • id: 103725764
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 630, 'group_order': 288, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 32, 'size': 2}
  • id: 103725765
    {'aut_label': '3A', 'centralizer': '2.a1.b1', 'counter': 8, 'group_counter': 630, 'group_order': 288, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 192, 'size': 2}
  • id: 103725766
    {'aut_label': '3C', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 630, 'group_order': 288, 'label': '3C', 'order': 3, 'powers': [9, 1], 'representative': 224, 'size': 4}
  • id: 103725726
    {'aut_label': '4A', 'centralizer': '12.e1.a1', 'counter': 10, 'group_counter': 630, 'group_order': 288, 'label': '4A', 'order': 4, 'powers': [3, 10], 'representative': 24, 'size': 12}
  • id: 103725727
    {'aut_label': '4B', 'centralizer': '12.f1.b1', 'counter': 11, 'group_counter': 630, 'group_order': 288, 'label': '4B', 'order': 4, 'powers': [4, 11], 'representative': 6, 'size': 12}
  • id: 103725728
    {'aut_label': '4B', 'centralizer': '12.f1.a1', 'counter': 12, 'group_counter': 630, 'group_order': 288, 'label': '4C', 'order': 4, 'powers': [4, 12], 'representative': 77, 'size': 12}
  • id: 103725729
    {'aut_label': '4A', 'centralizer': '12.e1.b1', 'counter': 13, 'group_counter': 630, 'group_order': 288, 'label': '4D', 'order': 4, 'powers': [3, 13], 'representative': 51, 'size': 12}
  • id: 103725730
    {'aut_label': '4E', 'centralizer': '18.b1.a1', 'counter': 14, 'group_counter': 630, 'group_order': 288, 'label': '4E', 'order': 4, 'powers': [4, 14], 'representative': 207, 'size': 18}
  • id: 103725731
    {'aut_label': '4E', 'centralizer': '18.b1.a1', 'counter': 15, 'group_counter': 630, 'group_order': 288, 'label': '4F', 'order': 4, 'powers': [4, 15], 'representative': 27, 'size': 18}
  • id: 103725732
    {'aut_label': '4G1', 'centralizer': '18.b1.a1', 'counter': 16, 'group_counter': 630, 'group_order': 288, 'label': '4G1', 'order': 4, 'powers': [4, 17], 'representative': 62, 'size': 18}
  • id: 103725733
    {'aut_label': '4G1', 'centralizer': '18.b1.a1', 'counter': 17, 'group_counter': 630, 'group_order': 288, 'label': '4G-1', 'order': 4, 'powers': [4, 16], 'representative': 58, 'size': 18}
  • id: 103725734
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 18, 'group_counter': 630, 'group_order': 288, 'label': '6A', 'order': 6, 'powers': [7, 2], 'representative': 20, 'size': 2}
  • id: 103725735
    {'aut_label': '6A', 'centralizer': '2.a1.b1', 'counter': 19, 'group_counter': 630, 'group_order': 288, 'label': '6B', 'order': 6, 'powers': [8, 2], 'representative': 148, 'size': 2}
  • id: 103725737
    {'aut_label': '6C', 'centralizer': '2.a1.a1', 'counter': 20, 'group_counter': 630, 'group_order': 288, 'label': '6C', 'order': 6, 'powers': [7, 3], 'representative': 16, 'size': 2}
  • id: 103725738
    {'aut_label': '6D', 'centralizer': '2.a1.b1', 'counter': 21, 'group_counter': 630, 'group_order': 288, 'label': '6D', 'order': 6, 'powers': [8, 4], 'representative': 196, 'size': 2}
  • id: 103725739
    {'aut_label': '6D', 'centralizer': '2.a1.a1', 'counter': 22, 'group_counter': 630, 'group_order': 288, 'label': '6E', 'order': 6, 'powers': [7, 4], 'representative': 68, 'size': 2}
  • id: 103725740
    {'aut_label': '6C', 'centralizer': '2.a1.b1', 'counter': 23, 'group_counter': 630, 'group_order': 288, 'label': '6F', 'order': 6, 'powers': [8, 3], 'representative': 240, 'size': 2}
  • id: 103725741
    {'aut_label': '6G', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 630, 'group_order': 288, 'label': '6G', 'order': 6, 'powers': [9, 3], 'representative': 112, 'size': 4}
  • id: 103725742
    {'aut_label': '6H', 'centralizer': '4.a1.a1', 'counter': 25, 'group_counter': 630, 'group_order': 288, 'label': '6H', 'order': 6, 'powers': [8, 5], 'representative': 97, 'size': 4}
  • id: 103725743
    {'aut_label': '6H', 'centralizer': '4.a1.a1', 'counter': 26, 'group_counter': 630, 'group_order': 288, 'label': '6I', 'order': 6, 'powers': [7, 5], 'representative': 33, 'size': 4}
  • id: 103725744
    {'aut_label': '6H', 'centralizer': '4.a1.a1', 'counter': 27, 'group_counter': 630, 'group_order': 288, 'label': '6J', 'order': 6, 'powers': [7, 6], 'representative': 17, 'size': 4}
  • id: 103725745
    {'aut_label': '6K', 'centralizer': '4.a1.a1', 'counter': 28, 'group_counter': 630, 'group_order': 288, 'label': '6K', 'order': 6, 'powers': [9, 4], 'representative': 132, 'size': 4}
  • id: 103725746
    {'aut_label': '6L', 'centralizer': '4.a1.a1', 'counter': 29, 'group_counter': 630, 'group_order': 288, 'label': '6L', 'order': 6, 'powers': [9, 2], 'representative': 116, 'size': 4}
  • id: 103725748
    {'aut_label': '6M', 'centralizer': '4.a1.a1', 'counter': 30, 'group_counter': 630, 'group_order': 288, 'label': '6M', 'order': 6, 'powers': [9, 5], 'representative': 129, 'size': 4}
  • id: 103725749
    {'aut_label': '6M', 'centralizer': '4.a1.a1', 'counter': 31, 'group_counter': 630, 'group_order': 288, 'label': '6N', 'order': 6, 'powers': [9, 6], 'representative': 113, 'size': 4}
  • id: 103725750
    {'aut_label': '6H', 'centralizer': '4.a1.a1', 'counter': 32, 'group_counter': 630, 'group_order': 288, 'label': '6O', 'order': 6, 'powers': [8, 6], 'representative': 101, 'size': 4}
  • id: 103725751
    {'aut_label': '6M', 'centralizer': '4.a1.a1', 'counter': 33, 'group_counter': 630, 'group_order': 288, 'label': '6P', 'order': 6, 'powers': [9, 5], 'representative': 225, 'size': 4}
  • id: 103725752
    {'aut_label': '6M', 'centralizer': '4.a1.a1', 'counter': 34, 'group_counter': 630, 'group_order': 288, 'label': '6Q', 'order': 6, 'powers': [9, 6], 'representative': 209, 'size': 4}
  • id: 103725753
    {'aut_label': '12A1', 'centralizer': '12.e1.a1', 'counter': 35, 'group_counter': 630, 'group_order': 288, 'label': '12A1', 'order': 12, 'powers': [20, 10], 'representative': 8, 'size': 12}
  • id: 103725754
    {'aut_label': '12A1', 'centralizer': '12.e1.a1', 'counter': 36, 'group_counter': 630, 'group_order': 288, 'label': '12A5', 'order': 12, 'powers': [20, 10], 'representative': 40, 'size': 12}
  • id: 103725755
    {'aut_label': '12B1', 'centralizer': '12.f1.b1', 'counter': 37, 'group_counter': 630, 'group_order': 288, 'label': '12B1', 'order': 12, 'powers': [21, 11], 'representative': 98, 'size': 12}
  • id: 103725756
    {'aut_label': '12B1', 'centralizer': '12.f1.b1', 'counter': 38, 'group_counter': 630, 'group_order': 288, 'label': '12B5', 'order': 12, 'powers': [21, 11], 'representative': 194, 'size': 12}
  • id: 103725757
    {'aut_label': '12B1', 'centralizer': '12.f1.a1', 'counter': 39, 'group_counter': 630, 'group_order': 288, 'label': '12C1', 'order': 12, 'powers': [22, 12], 'representative': 9, 'size': 12}
  • id: 103725759
    {'aut_label': '12B1', 'centralizer': '12.f1.a1', 'counter': 40, 'group_counter': 630, 'group_order': 288, 'label': '12C5', 'order': 12, 'powers': [22, 12], 'representative': 41, 'size': 12}
  • id: 103725760
    {'aut_label': '12A1', 'centralizer': '12.e1.b1', 'counter': 41, 'group_counter': 630, 'group_order': 288, 'label': '12D1', 'order': 12, 'powers': [23, 13], 'representative': 99, 'size': 12}
  • id: 103725761
    {'aut_label': '12A1', 'centralizer': '12.e1.b1', 'counter': 42, 'group_counter': 630, 'group_order': 288, 'label': '12D5', 'order': 12, 'powers': [23, 13], 'representative': 195, 'size': 12}
• 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: 2448313
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1a', '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], 'schur_index': 1}
  • id: 2448324
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1b', '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], 'schur_index': 1}
  • id: 2448335
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 2448344
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 2448345
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2448346
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2448347
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 2448348
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 2448349
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 0, 2, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, 0, 0, -1, -1, 0, -1], 'schur_index': 1}
  • id: 2448314
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, 0, 2, 0, 2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, -1, -1, -1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 2448315
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, 2, 0, 0, -2, -2, 2, -2, -2, 2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448316
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, 0, 0, -2, -2, 2, -2, -2, 2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448317
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, 2, -1, -2, 0, 2, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, 2, 1, 1, 1, -1, 1, -1, -1, -2, -2, 1, 1, -1, 0, 0, 0, -1, 1, 0, 1], 'schur_index': 1}
  • id: 2448318
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, 2, -1, 2, 0, -2, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, 2, 1, 1, 1, -1, 1, -1, -1, -2, -2, 1, 1, 1, 0, 0, 0, 1, -1, 0, -1], 'schur_index': 1}
  • id: 2448319
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -1, -1, 0, -2, 0, 2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -2, 1, 1, -1, 1, -1, -1, 1, 1, 1, -2, 0, -1, 1, 1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 2448320
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -1, -1, 0, 2, 0, -2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -2, 1, 1, -1, 1, -1, -1, 1, 1, 1, -2, 0, 1, -1, -1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 2448321
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, 2, -1, -2, 0, -2, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 1, 0, 0, 0, 1, 1, 0, 1], 'schur_index': 1}
  • id: 2448322
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, 0, -2, 0, -2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 1, 1, 1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 2448323
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2k', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448325
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2l', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448326
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2m', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, 0, 0, 0, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448327
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2n', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -2, 4, -4, 2, 2, -2, -2, 2, 2, 2, -4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448328
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2o', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, 4, -2, 2, -4, 2, -2, -2, 2, 2, 2, 2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448329
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2p', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -2, 4, -4, -2, -2, 2, -2, -2, 2, 2, 4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448330
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.2q', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, 4, -2, 2, 4, -2, 2, -2, -2, 2, 2, -2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448331
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448332
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -2, 2, -4, 4, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448333
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 4, -4, 2, -2, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448334
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4d', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, -1, -1, 1, -1, 1, 1, 2, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448336
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4e', 'multiplicity': 1, 'nt': [12, 81], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 0, -3, 3, -1, 3, -1, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448337
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4f', 'multiplicity': 1, 'nt': [12, 81], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 0, 3, -3, -1, -3, -1, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2448338
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4g', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, 2, -4, -4, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448339
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4h', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -4, -4, 2, 2, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448340
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4i', 'multiplicity': 1, 'nt': [24, 62], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, -1, 1, 1, -1, -1, -1, 2, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448341
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4j', 'multiplicity': 1, 'nt': [24, 62], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, -2, 1, -1, 1, 1, -1, -1, -2, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448342
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4k', 'multiplicity': 1, 'nt': [24, 206], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, -3, -3, -1, 3, 1, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2448343
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '288.630', 'group_order': 288, 'image': None, 'label': '288.630.4l', 'multiplicity': 1, 'nt': [24, 206], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, 3, 3, -1, -3, 1, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 3131823
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 288, 'label': '288.630.1a', '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]]]}
  • id: 3131834
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 144, 'label': '288.630.1b', '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]]]}
  • id: 3131845
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 144, 'label': '288.630.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3131856
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 144, 'label': '288.630.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3131860
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 144, 'label': '288.630.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 3131861
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 144, 'label': '288.630.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3131862
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 144, 'label': '288.630.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 3131863
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 288, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 144, 'label': '288.630.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 3131864
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 48, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 48, 'label': '288.630.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 3131824
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 48, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 48, 'label': '288.630.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 3131825
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 72, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.b1', 'kernel_order': 36, 'label': '288.630.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131826
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 72, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 36, 'label': '288.630.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131827
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 48, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.b1', 'kernel_order': 24, 'label': '288.630.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 3131828
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 48, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.b1', 'kernel_order': 24, 'label': '288.630.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 3131829
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 48, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 24, 'label': '288.630.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 3131830
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 48, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 24, 'label': '288.630.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 3131831
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 48, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 24, 'label': '288.630.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 3131832
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 48, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 24, 'label': '288.630.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 3131833
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 72, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.b1.b1', 'kernel_order': 36, 'label': '288.630.2k', 'nt': [8, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131835
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 72, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.b1.a1', 'kernel_order': 36, 'label': '288.630.2l', 'nt': [8, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131836
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 72, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 18, 'label': '288.630.2m1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131837
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 72, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 18, 'label': '288.630.2m2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131838
    {'center': '12.a1.b1', 'center_index': 12, 'center_order': 24, 'counter': 23, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.d1', 'kernel_order': 12, 'label': '288.630.2n1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]]]}
  • id: 3131839
    {'center': '12.a1.b1', 'center_index': 12, 'center_order': 24, 'counter': 24, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.d1', 'kernel_order': 12, 'label': '288.630.2n2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]]]}
  • id: 3131840
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.c1', 'kernel_order': 12, 'label': '288.630.2o1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]]]}
  • id: 3131841
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.c1', 'kernel_order': 12, 'label': '288.630.2o2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 3131842
    {'center': '12.a1.b1', 'center_index': 12, 'center_order': 24, 'counter': 27, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.b1', 'kernel_order': 12, 'label': '288.630.2p1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]]]}
  • id: 3131843
    {'center': '12.a1.b1', 'center_index': 12, 'center_order': 24, 'counter': 28, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.b1', 'kernel_order': 12, 'label': '288.630.2p2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]]]}
  • id: 3131844
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 24, 'counter': 29, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.a1', 'kernel_order': 12, 'label': '288.630.2q1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]]]}
  • id: 3131846
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 24, 'counter': 30, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.b1.a1', 'kernel_order': 12, 'label': '288.630.2q2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 3131847
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 8, 'label': '288.630.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131848
    {'center': '24.a1.b1', 'center_index': 24, 'center_order': 12, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.b1', 'kernel_order': 6, 'label': '288.630.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131849
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 12, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 6, 'label': '288.630.4c', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131850
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 4, 'label': '288.630.4d', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131851
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '144.154', 'image_order': 144, 'indicator': 1, 'kernel': '144.c1.a1', 'kernel_order': 2, 'label': '288.630.4e', 'nt': [12, 81], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131852
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '144.154', 'image_order': 144, 'indicator': 1, 'kernel': '144.c1.a1', 'kernel_order': 2, 'label': '288.630.4f', 'nt': [12, 81], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131853
    {'center': '24.a1.b1', 'center_index': 24, 'center_order': 12, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.b1.b1', 'kernel_order': 6, 'label': '288.630.4g', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131854
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 12, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.b1.a1', 'kernel_order': 6, 'label': '288.630.4h', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131855
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 8, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '72.24', 'image_order': 72, 'indicator': -1, 'kernel': '72.b1.b1', 'kernel_order': 4, 'label': '288.630.4i', 'nt': [24, 62], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131857
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 8, 'counter': 40, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '72.24', 'image_order': 72, 'indicator': -1, 'kernel': '72.b1.a1', 'kernel_order': 4, 'label': '288.630.4j', 'nt': [24, 62], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131858
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '144.148', 'image_order': 144, 'indicator': -1, 'kernel': '144.b1.a1', 'kernel_order': 2, 'label': '288.630.4k', 'nt': [24, 206], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3131859
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 4, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.630', 'group_counter': 630, 'group_order': 288, 'image': None, 'image_isoclass': '144.148', 'image_order': 144, 'indicator': -1, 'kernel': '144.b1.a1', 'kernel_order': 2, 'label': '288.630.4l', 'nt': [24, 206], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 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: 51646258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '288.630.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.630', 'subgroup_hash': 630, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.176', 'subgroup_hash': 176, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.152', 'subgroup_hash': 152, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], '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: 51646281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51646292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51646314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 72, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 72, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51646353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51646354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51646355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646364
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646365
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646366
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '288.630.9.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 2}
  • id: 51646379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], '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: 51646380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51646382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.12.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 51646412
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 51646413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 51646414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.24.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 51646260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646262
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646263
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646264
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646265
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646266
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646267
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646273
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51646275
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646276
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646277
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646278
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646279
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646280
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646282
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646283
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646284
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646285
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646286
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646287
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.24.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646288
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '288.630.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 51646289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['U0'], '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: 51646290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646293
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646295
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646296
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646298
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 51646301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 138, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', '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: 51646302
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 139, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', '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: 51646304
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 140, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': 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: 51646305
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 141, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': 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: 51646306
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 142, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646307
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 143, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646308
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646309
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646310
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646311
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646312
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646313
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 150, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646317
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646318
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646319
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.48.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51646320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.630.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': 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: 51646324
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': 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: 51646326
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': 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: 51646327
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.630.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51646328
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646329
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646330
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646331
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646332
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51646333
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.85', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 85, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_6', 'simple': 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: 51646334
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.96.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.85', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 85, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], '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: 51646335
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 51646337
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 2, 'counter': 170, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.152', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 152, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51646338
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 2, 'counter': 171, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.148', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 148, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6.D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51646339
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 2, 'counter': 172, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.630.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.154', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 154, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51646340
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 51646341
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.630.144.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, '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: 51646342
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.630', 'ambient_counter': 630, 'ambient_order': 288, 'ambient_tex': 'C_6^2:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 1, 'counter': 175, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '288.630.288.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': True, 'proper': False, 'quotient': '288.630', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 630, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', '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: 51646258
    {'ambient': '288.630', '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': '72.a1.a1', 'complements': ['288.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '3.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7431, 5530, 3652, 3496, 7362, 4222, 2563, 3803], 'generators': [1, 32, 48, 2, 96, 24, 52], 'label': '288.630.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '72.46', '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': '72.46'}
  • id: 51646259
    {'ambient': '288.630', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.b1', '6.b1.b1', '6.c1.b1', '6.e1.b1', '6.f1.b1', '6.g1.b1', '6.h1.b1', '9.a1.a1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7626, -1, 3405, -1, 7590, -1, 1923, -1], 'generators': [1, 96, 48, 2, 24, 52], 'label': '288.630.3.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '3.a1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646260
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.g1.c1', '72.c1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4067, -1, 1823, -1, 3845, -1, 8235, -1], 'generators': [1, 48, 32], 'label': '288.630.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '144.148', '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': '2.1'}
  • id: 51646261
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.b1'], 'contains': ['48.b1.b1', '48.g1.b1', '48.g1.d1', '72.c1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4067, -1, 860, -1, 3845, -1, 7486, -1], 'generators': [1, 48, 96], 'label': '288.630.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.e1.b1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646262
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1'], 'contains': ['48.e1.a1', '48.h1.a1', '48.h1.d1', '72.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [991, -1, 3595, -1, 1580, -1, 9732, -1], 'generators': [1, 48, 128], 'label': '288.630.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '144.148', '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': '2.1'}
  • id: 51646263
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1'], 'contains': ['48.e1.a1', '48.h1.b1', '48.h1.c1', '72.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [991, -1, 3133, -1, 1580, -1, 9545, -1], 'generators': [1, 48, 224], 'label': '288.630.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.b1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646264
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.e1.a1'], 'contains': ['48.b1.a1', '72.d1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9764, -1, 276, -1, 9262, -1, 1315, -1], 'generators': [24, 32, 48], 'label': '288.630.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.g1.a1', 'projective_image': '144.148', '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': '2.1'}
  • id: 51646265
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.e1.b1'], 'contains': ['48.b1.b1', '72.d1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9764, -1, 163, -1, 9262, -1, 612, -1], 'generators': [3, 96, 48], 'label': '288.630.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '24.g1.b1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646266
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.d1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9233, -1, 441, -1, 8919, -1, 902, -1], 'generators': [3, 48, 32], 'label': '288.630.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.h1.a1', 'projective_image': '144.148', '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': '12.4'}
  • id: 51646267
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.b1'], 'contains': ['48.b1.b1', '72.d1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9233, -1, 48, -1, 8919, -1, 1168, -1], 'generators': [24, 48, 96], 'label': '288.630.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.h1.b1', 'projective_image': '144.148', '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': '12.4'}
  • id: 51646268
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.g1.c1', '72.e1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3702, -1, 7861, -1, 4201, -1, 6924, -1], 'generators': [1, 4, 32], 'label': '288.630.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646269
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.b1', '12.k1.c1', '12.k1.d1'], 'contains': ['48.c1.b1', '48.g1.b1', '48.g1.d1', '72.e1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3702, -1, 7053, -1, 4201, -1, 6624, -1], 'generators': [1, 4, 96], 'label': '288.630.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.i1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646270
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.d1.a1', '8.f1.a1', '12.a1.a1', '12.a1.b1', '12.d1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3012, 3964, 2889, 7338, 1764, 8125, 8451, 7830], 'generators': [1, 96, 52, 48, 32], 'label': '288.630.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646271
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.l1.a1', '12.l1.c1'], 'contains': ['48.f1.a1', '48.h1.a1', '48.h1.c1', '72.e1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [523, -1, 8576, -1, 1937, -1, 8609, -1], 'generators': [1, 4, 128], 'label': '288.630.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646272
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.l1.b1', '12.l1.d1'], 'contains': ['48.f1.a1', '48.h1.b1', '48.h1.d1', '72.e1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [523, -1, 9348, -1, 1937, -1, 8422, -1], 'generators': [1, 4, 224], 'label': '288.630.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.j1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646273
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '12.f1.a1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.c1.a1', '72.f1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6204, -1, 6418, -1, 6618, -1, 3707, -1], 'generators': [77, 32, 4], 'label': '288.630.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.k1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646274
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.f1.b1', '12.m1.c1', '12.m1.d1'], 'contains': ['48.c1.b1', '72.f1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6204, -1, 5979, -1, 6618, -1, 3134, -1], 'generators': [2, 96, 4], 'label': '288.630.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '24.k1.b1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646275
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.c1.a1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.c1.a1', '72.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6445, -1, 6637, -1, 6854, -1, 3583, -1], 'generators': [2, 4, 32], 'label': '288.630.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.l1.a1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646276
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '12.c1.b1', '12.m1.c1', '12.m1.d1'], 'contains': ['48.c1.b1', '72.f1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6445, -1, 5864, -1, 6854, -1, 3456, -1], 'generators': [77, 4, 96], 'label': '288.630.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.l1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646277
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.a1', '12.k1.a1', '12.m1.a1'], 'contains': ['48.c1.a1', '72.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5130, -1, 7715, -1, 5313, -1, 5020, -1], 'generators': [11, 4, 32], 'label': '288.630.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646278
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.g1.a1', '12.k1.b1', '12.m1.b1'], 'contains': ['48.c1.a1', '72.g1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5130, -1, 7533, -1, 5313, -1, 5334, -1], 'generators': [59, 4, 32], 'label': '288.630.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.b1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646279
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.b1', '12.k1.c1', '12.m1.c1'], 'contains': ['48.c1.b1', '72.g1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5130, -1, 7248, -1, 5313, -1, 4767, -1], 'generators': [11, 4, 96], 'label': '288.630.24.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.m1.c1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646280
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.g1.b1', '12.k1.d1', '12.m1.d1'], 'contains': ['48.c1.b1', '72.g1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5130, -1, 6857, -1, 5313, -1, 4893, -1], 'generators': [59, 4, 96], 'label': '288.630.24.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.m1.d1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646281
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '12.b1.b1', '12.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8829, 2328, 2362, 1537, 8940, 6564, 1344, 2718], 'generators': [52, 96, 24, 32, 48], 'label': '288.630.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646282
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.h1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['48.c1.a1', '72.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4884, -1, 8326, -1, 5071, -1, 5587, -1], 'generators': [10, 4, 32], 'label': '288.630.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.n1.a1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646283
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.h1.b1', '12.k1.c1', '12.k1.d1'], 'contains': ['48.c1.b1', '72.h1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4884, -1, 7366, -1, 5071, -1, 5460, -1], 'generators': [10, 4, 96], 'label': '288.630.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '24.n1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646284
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.i1.a1', '12.l1.a1', '12.l1.b1'], 'contains': ['48.f1.a1', '72.g1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2623, -1, 9805, -1, 3546, -1, 5901, -1], 'generators': [11, 4, 128], 'label': '288.630.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.o1.a1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646285
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.i1.a1', '12.l1.c1', '12.l1.d1'], 'contains': ['48.f1.a1', '72.g1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2623, -1, 8848, -1, 3546, -1, 6214, -1], 'generators': [59, 4, 128], 'label': '288.630.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.o1.b1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646286
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.j1.a1', '12.l1.a1', '12.l1.d1'], 'contains': ['48.f1.a1', '72.h1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1398, -1, 9653, -1, 2592, -1, 6341, -1], 'generators': [10, 4, 128], 'label': '288.630.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.p1.a1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646287
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.j1.a1', '12.l1.b1', '12.l1.c1'], 'contains': ['48.f1.a1', '72.h1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1398, -1, 9118, -1, 2592, -1, 6468, -1], 'generators': [10, 4, 224], 'label': '288.630.24.p1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.p1.a2', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646288
    {'ambient': '288.630', 'aut_centralizer_order': 576, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.d1.b1'], 'contains': ['96.a1.a1', '96.a1.b1', '96.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2754, 7096, 1231, 3960, 2500, 4154, 7541, 3858], 'generators': [32, 96], 'label': '288.630.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.c1.a1', '16.a1.a1'], 'normal_contains': ['96.a1.a1', '96.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '288.630', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646289
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.a1.b1', '12.d1.a1', '18.a1.a1', '18.a1.b1', '18.b1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.b1.b1', '72.c1.a1', '72.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5379, 2530, 3414, 7484, 4487, 8896, 6774, 8167], 'generators': [1, 52, 48], 'label': '288.630.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.a1.b1'], 'normal_contains': ['72.a1.a1', '72.b1.a1', '72.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646290
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.e1.a1', '18.a1.a1', '18.c1.a1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8765, -1, 2501, -1, 8599, -1, 1656, -1], 'generators': [52, 24], 'label': '288.630.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646291
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.b1', '18.a1.b1', '18.c1.b1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.d1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8765, -1, 2731, -1, 8599, -1, 1469, -1], 'generators': [3, 52], 'label': '288.630.36.b1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.b1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646292
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.b1', '12.b1.a1', '12.e1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8829, 2328, 2632, 3801, 8940, 6564, 859, 5738], 'generators': [3, 32, 52, 96, 48], 'label': '288.630.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646293
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.f1.b1', '18.a1.b1', '18.c1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7750, -1, 4643, -1, 7362, -1, 2368, -1], 'generators': [2, 48], 'label': '288.630.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.c1.a1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646294
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.f1.a1', '18.a1.a1', '18.c1.b1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.f1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7750, -1, 4112, -1, 7362, -1, 2577, -1], 'generators': [77, 48], 'label': '288.630.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646295
    {'ambient': '288.630', 'aut_centralizer_order': 128, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.g1.b1', '12.i1.a1', '18.b1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.g1.a1', '72.g1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5978, -1, 5350, -1, 5968, -1, 4423, -1], 'generators': [11, 48], 'label': '288.630.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '72.46', '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': '2.1'}
  • id: 51646296
    {'ambient': '288.630', 'aut_centralizer_order': 128, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.h1.b1', '12.j1.a1', '18.b1.a1', '18.c1.a1', '18.c1.b1'], 'contains': ['72.a1.a1', '72.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6343, -1, 5054, -1, 5611, -1, 4610, -1], 'generators': [10, 48], 'label': '288.630.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '72.46', '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': '2.1'}
  • id: 51646297
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.k1.c1', '12.l1.a1', '12.l1.b1', '18.b1.a1'], 'contains': ['72.e1.a1', '72.g1.a1', '72.h1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4067, -1, 8356, -1, 4773, -1, 5744, -1], 'generators': [1, 10], 'label': '288.630.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.a1', 'projective_image': '144.154', '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': '1.1'}
  • id: 51646298
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '12.k1.d1', '12.l1.c1', '12.l1.d1', '18.b1.a1'], 'contains': ['72.e1.a1', '72.g1.b1', '72.h1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4067, -1, 8036, -1, 4773, -1, 6057, -1], 'generators': [49, 10], 'label': '288.630.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646299
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.m1.c1', '18.e1.a1'], 'contains': ['72.f1.a1', '72.f1.b1', '72.g1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6940, -1, 6206, -1, 7068, -1, 3244, -1], 'generators': [29, 2], 'label': '288.630.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.g1.a1', 'projective_image': '144.154', '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': '4.2'}
  • id: 51646300
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '12.m1.d1', '18.e1.a1'], 'contains': ['72.f1.a1', '72.f1.b1', '72.g1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6940, -1, 6003, -1, 7068, -1, 3344, -1], 'generators': [77, 2], 'label': '288.630.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.g1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646301
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.c1'], 'contains': ['96.a1.a1', '144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3555, 4671, 1546, 6365, 2702, 6419, 7746, 6214], 'generators': [52, 32], 'label': '288.630.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.c1'], 'normal_contains': ['96.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '144.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.7', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646302
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.b1', '24.b1.b1', '24.b1.d1'], 'contains': ['96.a1.b1', '144.a1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3555, 4671, 872, 5779, 2702, 6419, 7223, 5780], 'generators': [52, 96], 'label': '288.630.48.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': ['16.a1.a1', '24.a1.b1', '24.b1.b1', '24.b1.d1'], 'normal_contains': ['96.a1.b1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.b1', 'projective_image': '144.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.7', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646357
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.b1'], 'contains': ['12.c1.b1', '12.e1.b1', '12.h1.b1', '18.c1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8429, -1, 3579, -1, 8321, -1, 2083, -1], 'generators': [77, 96, 10, 4, 48], 'label': '288.630.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.e1.b1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646303
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '12.c1.a1', '12.f1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6698, 5601, 4891, 6066, 6233, 4954, 3315, 3725], 'generators': [2, 32, 48, 96, 4], 'label': '288.630.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646304
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.e1.a1', '24.g1.a1', '24.h1.a1'], 'contains': ['96.a1.a1', '144.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7348, 5570, 780, 4742, 5664, 5725, 4191, 4756], 'generators': [48, 32], 'label': '288.630.48.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '144.148', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646305
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.b1', '24.e1.b1', '24.g1.b1', '24.h1.b1'], 'contains': ['96.a1.b1', '144.b1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7348, 5570, 241, 2898, 5664, 5725, 4048, 4322], 'generators': [48, 96], 'label': '288.630.48.b1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': ['16.b1.a1', '24.a1.b1'], 'normal_contains': ['96.a1.b1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.b1', 'projective_image': '144.148', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646306
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.i1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1'], 'contains': ['96.a1.a1', '144.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4811, 6469, 7527, 3597, 5071, 5031, 5148, 3394], 'generators': [4, 32], 'label': '288.630.48.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '144.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '144.154', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646307
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.b1', '24.i1.b1', '24.k1.b1', '24.l1.b1', '24.m1.c1', '24.m1.d1', '24.n1.b1'], 'contains': ['96.a1.b1', '144.c1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4811, 6469, 6900, 2376, 5071, 5031, 4907, 2960], 'generators': [4, 96], 'label': '288.630.48.c1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.c1.b1', 'normal_contained_in': ['16.c1.a1', '24.a1.b1'], 'normal_contains': ['96.a1.b1', '144.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.b1', 'projective_image': '144.154', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646308
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['96.b1.a1', '144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [945, -1, 3544, -1, 1748, -1, 8481, -1], 'generators': [52, 128], 'label': '288.630.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '144.152', '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': '2.1'}
  • id: 51646309
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1'], 'contains': ['96.b1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2011, -1, 3403, -1, 2891, -1, 8156, -1], 'generators': [48, 128], 'label': '288.630.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.e1.a1', 'projective_image': '144.148', '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': '2.1'}
  • id: 51646310
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.c1.a1', '24.j1.a1', '24.j1.b1', '24.o1.a1', '24.o1.b1', '24.p1.a1', '24.p1.a2'], 'contains': ['96.b1.a1', '144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1807, -1, 8943, -1, 3079, -1, 6404, -1], 'generators': [4, 128], 'label': '288.630.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646311
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.e1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '144.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3265, -1, 2013, -1, 3454, -1, 8057, -1], 'generators': [1, 32], 'label': '288.630.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '288.630', '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: 51646312
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.b1', '24.e1.b1', '24.i1.b1'], 'contains': ['96.a1.b1', '144.d1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3265, -1, 1426, -1, 3454, -1, 7647, -1], 'generators': [1, 96], 'label': '288.630.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.b1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646313
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.b1.c1', '24.e1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '144.d1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3265, -1, 1708, -1, 3454, -1, 7958, -1], 'generators': [49, 32], 'label': '288.630.48.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.c1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646314
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.g1.b1', '12.c1.b1', '12.f1.a1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6698, 5601, 4677, 473, 6233, 4954, 3774, 4732], 'generators': [77, 96, 48, 32, 4], 'label': '288.630.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646315
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.b1.d1', '24.e1.b1', '24.i1.b1'], 'contains': ['96.a1.b1', '144.d1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3265, -1, 965, -1, 3454, -1, 7435, -1], 'generators': [49, 96], 'label': '288.630.48.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.d1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646316
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.f1.a1', '24.j1.a1'], 'contains': ['96.b1.a1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [752, -1, 3871, -1, 1937, -1, 9137, -1], 'generators': [1, 128], 'label': '288.630.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.h1.a1', 'projective_image': '288.630', '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': '2.1'}
  • id: 51646317
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.f1.b1', '24.j1.b1'], 'contains': ['96.b1.a1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [752, -1, 3730, -1, 1937, -1, 8983, -1], 'generators': [1, 224], 'label': '288.630.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.h1.b1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646318
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.d1.b1', '24.f1.b1', '24.j1.a1'], 'contains': ['96.b1.a1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [752, -1, 3311, -1, 1937, -1, 8631, -1], 'generators': [49, 224], 'label': '288.630.48.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.h1.c1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646319
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.d1.b1', '24.f1.a1', '24.j1.b1'], 'contains': ['96.b1.a1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [752, -1, 3637, -1, 1937, -1, 8774, -1], 'generators': [49, 128], 'label': '288.630.48.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.h1.d1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646320
    {'ambient': '288.630', 'aut_centralizer_order': 4608, 'aut_label': '72.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.b1', '24.c1.a1', '36.a1.a1', '36.b1.a1', '36.b1.b1', '36.c1.a1', '36.c1.b1', '36.d1.a1', '36.e1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6046, 3803, 4224, 5455, 5462, 7161, 4297, 5220], 'generators': [52, 48], 'label': '288.630.72.a1.a1', 'mobius_quo': 2, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.a1.b1', '36.a1.a1'], 'normal_contains': ['144.b1.a1', '144.c1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.46', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646321
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1.a1', 'complements': ['4.g1.a1', '4.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '144.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2848, 2975, 3101, 7433, 2285, 7951, 8375, 8493], 'generators': [1, 52], 'label': '288.630.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.b1.a1', '24.b1.b1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '144.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.7', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646322
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1.a1', 'complements': ['4.g1.b1', '4.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.c1', '24.b1.d1', '24.d1.b1', '36.a1.a1'], 'contains': ['144.a1.a1', '144.d1.b1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2848, 2975, 2841, 8057, 2285, 7951, 7852, 7101], 'generators': [49, 52], 'label': '288.630.72.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.b1', 'normal_contained_in': ['24.b1.c1', '24.b1.d1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.b1', 'projective_image': '144.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.7', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646323
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.f1.a1', '24.f1.b1', '36.a1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.d1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4003, -1, 2946, -1, 3845, -1, 8262, -1], 'generators': [1, 48], 'label': '288.630.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646324
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.b1', '36.b1.a1'], 'contains': ['144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9101, -1, 312, -1, 8759, -1, 1486, -1], 'generators': [24], 'label': '288.630.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '72.d1.a1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646325
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '12.g1.a1', '12.g1.b1', '12.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4899, 7399, 6675, 2668, 3850, 1427, 4794, 512], 'generators': [11, 96, 48, 4, 32], 'label': '288.630.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51646326
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.h1.a1', '36.b1.b1'], 'contains': ['144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9101, -1, 561, -1, 8759, -1, 1148, -1], 'generators': [3], 'label': '288.630.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '72.d1.b1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646327
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.b1', '24.j1.a1', '24.j1.b1', '36.a1.a1', '36.f1.a1', '36.f1.b1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.d1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3782, -1, 7464, -1, 4343, -1, 7329, -1], 'generators': [1, 4], 'label': '288.630.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.e1.a1', 'projective_image': '144.154', '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': '1.1'}
  • id: 51646328
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.l1.a1', '36.c1.a1', '36.g1.a1', '36.g1.b1'], 'contains': ['144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6792, -1, 6144, -1, 6854, -1, 3272, -1], 'generators': [2], 'label': '288.630.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '72.f1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646329
    {'ambient': '288.630', 'aut_centralizer_order': 192, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.l1.b1', '36.c1.b1', '36.g1.a1', '36.g1.b1'], 'contains': ['144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6792, -1, 5990, -1, 6854, -1, 3427, -1], 'generators': [77], 'label': '288.630.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '72.f1.b1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646330
    {'ambient': '288.630', 'aut_centralizer_order': 128, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.m1.c1', '24.o1.a1', '36.d1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5425, -1, 7362, -1, 5260, -1, 5020, -1], 'generators': [11], 'label': '288.630.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646331
    {'ambient': '288.630', 'aut_centralizer_order': 128, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.m1.d1', '24.o1.b1', '36.d1.a1', '36.f1.b1', '36.g1.b1'], 'contains': ['144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5425, -1, 7172, -1, 5260, -1, 5247, -1], 'generators': [59], 'label': '288.630.72.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.g1.b1', 'projective_image': '144.154', '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': '2.1'}
  • id: 51646332
    {'ambient': '288.630', 'aut_centralizer_order': 128, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.n1.b1', '24.p1.a1', '24.p1.a2', '36.e1.a1', '36.f1.a1', '36.f1.b1'], 'contains': ['144.c1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4403, -1, 8542, -1, 4883, -1, 5665, -1], 'generators': [10], 'label': '288.630.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.h1.a1', 'projective_image': '144.154', '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': '1.1'}
  • id: 51646333
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.a1', 'complements': ['3.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.g1.a1', '48.g1.c1'], 'contains': ['288.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3592, 6327, 1708, 4380, 3549, 5079, 7650, 4322], 'generators': [32], 'label': '288.630.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1', '48.c1.a1', '48.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '288.630', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.19', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646334
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.b1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.b1', '48.b1.b1', '48.c1.b1', '48.g1.b1', '48.g1.d1'], 'contains': ['288.a1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3592, 6327, 1085, 3031, 3549, 5079, 7435, 3888], 'generators': [96], 'label': '288.630.96.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.b1', 'normal_contained_in': ['32.a1.a1', '48.b1.b1', '48.c1.b1', '48.a1.b1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.b1', 'projective_image': '288.630', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.19', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646335
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.h1.a1', '48.h1.b1', '48.h1.c1', '48.h1.d1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1895, -1, 3583, -1, 2506, -1, 8481, -1], 'generators': [128], 'label': '288.630.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.b1.a1', 'projective_image': '288.630', '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: 51646336
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.a1.a1', '8.h1.a1', '12.h1.a1', '12.h1.b1', '12.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4395, 9298, 5128, 4933, 3357, 3239, 5312, 1646], 'generators': [10, 96, 48, 4, 32], 'label': '288.630.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51646337
    {'ambient': '288.630', 'aut_centralizer_order': 4608, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.a1.b1', '48.d1.a1', '72.a1.a1', '72.b1.a1', '72.b1.b1'], 'contains': ['288.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3316, 3762, 2727, 6167, 2702, 7161, 7749, 5997], 'generators': [52], 'label': '288.630.144.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.a1.b1', '72.a1.a1', '72.b1.a1', '72.b1.b1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '144.152', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.152', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646338
    {'ambient': '288.630', 'aut_centralizer_order': 4608, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.b1.b1', '48.e1.a1', '72.a1.a1', '72.c1.a1', '72.d1.a1', '72.d1.b1'], 'contains': ['288.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5753, 4721, 1420, 4914, 5360, 6467, 4245, 4756], 'generators': [48], 'label': '288.630.144.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['48.b1.a1', '48.b1.b1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '144.148', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.148', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646339
    {'ambient': '288.630', 'aut_centralizer_order': 4608, 'aut_label': '144.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.b1', '48.f1.a1', '72.a1.a1', '72.e1.a1', '72.f1.a1', '72.f1.b1', '72.g1.a1', '72.g1.b1', '72.h1.a1'], 'contains': ['288.a1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4653, 5449, 7172, 3687, 4977, 5773, 5148, 3424], 'generators': [4], 'label': '288.630.144.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.c1.a1', 'normal_contained_in': ['48.c1.a1', '48.c1.b1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '144.154', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.154', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646340
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.g1.b1', '48.h1.a1', '48.h1.b1', '72.b1.a1', '72.c1.a1', '72.e1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3015, -1, 3397, -1, 3360, -1, 8159, -1], 'generators': [1], 'label': '288.630.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '288.630', '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': '1.1'}
  • id: 51646341
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.c1', '48.g1.d1', '48.h1.c1', '48.h1.d1', '72.b1.b1', '72.c1.a1', '72.e1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3015, -1, 2901, -1, 3360, -1, 7904, -1], 'generators': [49], 'label': '288.630.144.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.d1.b1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646342
    {'ambient': '288.630', 'aut_centralizer_order': None, 'aut_label': '288.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': ['96.a1.a1', '96.a1.b1', '96.b1.a1', '144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '144.d1.b1'], 'contains': [], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3455, 5085, 2796, 4380, 3454, 6120, 7699, 4322], 'generators': [], 'label': '288.630.288.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['96.a1.a1', '96.a1.b1', '144.b1.a1', '144.c1.a1', '144.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51646343
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.h1.a1', '12.k1.a1', '12.k1.c1', '12.l1.a1', '12.l1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3890, -1, 8677, -1, 2865, -1, 6251, -1], 'generators': [1, 96, 10, 4, 32], 'label': '288.630.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.f1.a1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51646344
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.b1', '8.f1.a1', '8.h1.a1', '12.k1.b1', '12.k1.d1', '12.l1.c1', '12.l1.d1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3890, -1, 7834, -1, 2865, -1, 6591, -1], 'generators': [49, 96, 10, 4, 32], 'label': '288.630.4.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.f1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51646345
    {'ambient': '288.630', 'aut_centralizer_order': 12, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.b1', '6.a1.b1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7235, 2520, 2863, 621, 7137, 7180, 2965, 5594], 'generators': [1, 96, 48, 24, 32, 52], 'label': '288.630.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.b1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646346
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.889', 'aut_weyl_index': 16, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.g1.b1', '12.m1.a1', '12.m1.c1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5995, -1, 6480, -1, 5865, -1, 3967, -1], 'generators': [29, 96, 2, 4, 32], 'label': '288.630.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.g1.a1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51646347
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.889', 'aut_weyl_index': 16, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.c1.b1', '8.g1.a1', '8.g1.b1', '12.m1.b1', '12.m1.d1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5995, -1, 6261, -1, 5865, -1, 4122, -1], 'generators': [77, 96, 2, 4, 32], 'label': '288.630.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.g1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51646348
    {'ambient': '288.630', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '18.a1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6510, 1298, 3273, 6390, 7504, 9330, 2229, 7077], 'generators': [1, 32, 2, 52, 48], 'label': '288.630.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.b1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646349
    {'ambient': '288.630', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '12.b1.b1', '12.c1.b1', '18.a1.a1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6510, 1298, 2355, 881, 7504, 9330, 2647, 6522], 'generators': [1, 96, 24, 52, 48], 'label': '288.630.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.b1', '12.b1.b1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646350
    {'ambient': '288.630', 'aut_centralizer_order': 24, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '18.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7103, -1, 3093, -1, 7137, -1, 2840, -1], 'generators': [1, 48, 24, 32, 52], 'label': '288.630.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646351
    {'ambient': '288.630', 'aut_centralizer_order': 24, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.b1'], 'contains': ['12.a1.b1', '12.e1.b1', '12.f1.b1', '18.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7103, -1, 2617, -1, 7137, -1, 1589, -1], 'generators': [1, 48, 2, 96, 52], 'label': '288.630.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.b1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646352
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '12.k1.a1', '12.k1.b1', '18.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5514, -1, 5896, -1, 4953, -1, 5570, -1], 'generators': [1, 32, 10, 48, 4], 'label': '288.630.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646353
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '12.g1.b1', '12.h1.b1', '12.k1.c1', '12.k1.d1', '18.b1.a1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5514, -1, 5378, -1, 4953, -1, 5053, -1], 'generators': [1, 96, 10, 48, 4], 'label': '288.630.6.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.c1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646354
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.d1.a1', '12.i1.a1', '12.j1.a1', '12.l1.a1', '12.l1.b1', '12.l1.c1', '12.l1.d1', '18.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1517, -1, 8904, -1, 2372, -1, 7322, -1], 'generators': [1, 128, 10, 48, 4], 'label': '288.630.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '6.d1.a1', 'projective_image': '72.46', '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': '6.1'}
  • id: 51646355
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.h1.a1', '18.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8429, -1, 4084, -1, 8321, -1, 2375, -1], 'generators': [2, 32, 24, 4, 48], 'label': '288.630.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646356
    {'ambient': '288.630', 'aut_centralizer_order': 12, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.c1.a1', '6.a1.a1', '6.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7235, 2520, 3165, 6714, 7137, 7180, 2161, 6600], 'generators': [1, 32, 48, 2, 96, 52], 'label': '288.630.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646358
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.h1.a1', '18.c1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8142, -1, 3925, -1, 8044, -1, 2521, -1], 'generators': [77, 32, 10, 4, 48], 'label': '288.630.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646359
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.b1'], 'contains': ['12.b1.b1', '12.f1.b1', '12.h1.b1', '18.c1.a1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8142, -1, 3746, -1, 8044, -1, 1782, -1], 'generators': [2, 96, 24, 4, 48], 'label': '288.630.6.f1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.f1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646360
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1', '18.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8778, -1, 2796, -1, 8599, -1, 1165, -1], 'generators': [3, 32, 24, 4, 48], 'label': '288.630.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646361
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.b1'], 'contains': ['12.b1.b1', '12.e1.b1', '12.g1.b1', '18.d1.a1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8778, -1, 2033, -1, 8599, -1, 1038, -1], 'generators': [3, 96, 24, 4, 48], 'label': '288.630.6.g1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.g1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646362
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1', '12.m1.a1', '12.m1.b1', '18.e1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7582, -1, 5627, -1, 6670, -1, 3544, -1], 'generators': [77, 32, 2, 48, 4], 'label': '288.630.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646363
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.b1'], 'contains': ['12.c1.b1', '12.f1.b1', '12.g1.b1', '12.m1.c1', '12.m1.d1', '18.e1.a1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7582, -1, 4414, -1, 6670, -1, 3085, -1], 'generators': [77, 96, 2, 48, 4], 'label': '288.630.6.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.h1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646364
    {'ambient': '288.630', 'aut_centralizer_order': 576, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1', '24.a1.b1', '24.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4376, 6197, 4761, 3603, 3059, 4173, 4630, 2592], 'generators': [52, 48, 32, 96], 'label': '288.630.8.a1.a1', 'mobius_quo': 2, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.a1.a1', '24.a1.a1', '24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646365
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '8.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.a1.a1', 'complements': ['36.g1.b1', '36.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '24.b1.a1', '24.b1.b1', '24.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1514, 3964, 1764, 7338, 828, 4964, 8954, 9500], 'generators': [1, 52, 32, 96], 'label': '288.630.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646366
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '8.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.a1.a1', 'complements': ['36.g1.a1', '36.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.b1', '24.b1.c1', '24.b1.d1', '24.d1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1514, 3964, 1014, 8102, 828, 4964, 8729, 7107], 'generators': [49, 52, 32, 96], 'label': '288.630.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.c1', '24.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646367
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.153182', 'aut_weyl_index': 4, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.f1.b1', '6.c1.a1', '6.c1.b1', '6.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4395, 9095, 5896, 5519, 3357, 4222, 5570, 952], 'generators': [1, 96, 32, 10, 48, 4], 'label': '288.630.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51646368
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 32, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.c1.a1', '24.m1.a1', '24.m1.c1', '24.o1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4741, 7822, 7883, 2262, 3750, 2140, 5223, 717], 'generators': [11, 4, 32, 96], 'label': '288.630.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '144.154', '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': '36.10'}
  • id: 51646369
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 32, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.c1.a1', '24.m1.b1', '24.m1.d1', '24.o1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4741, 7822, 7201, 2981, 3750, 2140, 5379, 1802], 'generators': [59, 4, 32, 96], 'label': '288.630.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '144.154', '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': '36.10'}
  • id: 51646370
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.d1.b1', '24.e1.a1', '24.e1.b1', '24.f1.a1', '24.f1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3080, -1, 1258, -1, 1457, -1, 8842, -1], 'generators': [1, 48, 32, 96], 'label': '288.630.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '144.148', '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': '2.1'}
  • id: 51646371
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '24.g1.a1', '24.h1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9842, -1, 402, -1, 9805, -1, 557, -1], 'generators': [24, 32, 48, 96], 'label': '288.630.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.e1.a1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646372
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.b1.a1', '24.g1.b1', '24.h1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9842, -1, 628, -1, 9805, -1, 103, -1], 'generators': [3, 96, 48, 32], 'label': '288.630.8.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.e1.b1', 'projective_image': '144.148', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646373
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.d1.b1', '24.i1.a1', '24.i1.b1', '24.j1.a1', '24.j1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2859, -1, 7619, -1, 1672, -1, 8616, -1], 'generators': [1, 4, 32, 96], 'label': '288.630.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646374
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.c1.a1', '24.k1.b1', '24.l1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5744, -1, 6825, -1, 6253, -1, 3516, -1], 'generators': [2, 96, 4, 32], 'label': '288.630.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.g1.a1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646375
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.c1.a1', '24.k1.a1', '24.l1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5744, -1, 6514, -1, 6253, -1, 4000, -1], 'generators': [77, 32, 4, 96], 'label': '288.630.8.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.g1.b1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646376
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 32, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.c1.a1', '24.n1.a1', '24.n1.b1', '24.p1.a1', '24.p1.a2'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3806, -1, 8399, -1, 2802, -1, 6210, -1], 'generators': [10, 4, 32, 96], 'label': '288.630.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.h1.a1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51646377
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.b1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.b1.a1', '18.c1.a1', '18.c1.b1', '18.d1.a1', '18.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8311, -1, 3415, -1, 7773, -1, 1923, -1], 'generators': [1, 2, 24], 'label': '288.630.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '72.46', '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': '8.5'}
  • id: 51646378
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 8, 'centralizer': '72.a1.a1', 'complements': ['144.d1.a1', '144.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '6.e1.a1', '6.f1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7847, 5530, 4129, 4475, 8012, 5802, 2358, 2875], 'generators': [2, 96, 32, 24, 4, 48], 'label': '288.630.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51646379
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.c1', '24.e1.a1', '24.i1.a1', '36.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 702, 3142, 8725, 4104, 9330, 8451, 8776], 'generators': [1, 52, 48, 32], 'label': '288.630.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.b1.c1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646380
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.b1', '6.b1.b1', '6.c1.b1'], 'contains': ['24.a1.b1', '24.b1.b1', '24.b1.d1', '24.e1.b1', '24.i1.b1', '36.a1.a1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 702, 2222, 6753, 4104, 9330, 8235, 7830], 'generators': [1, 52, 48, 96], 'label': '288.630.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.a1', '6.a1.b1'], 'normal_contains': ['24.a1.b1', '24.b1.b1', '24.b1.d1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646381
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '36.b1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9095, 2338, 2787, 4418, 8940, 7768, 787, 6359], 'generators': [3, 52, 48, 32], 'label': '288.630.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646382
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.b1', '6.f1.b1', '6.g1.b1'], 'contains': ['24.a1.b1', '24.h1.b1', '36.b1.a1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9095, 2338, 1511, 1587, 8940, 7768, 1144, 3339], 'generators': [52, 24, 48, 96], 'label': '288.630.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.b1.a1', '6.a1.b1'], 'normal_contains': ['24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646383
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.e1.a1', '6.h1.a1'], 'contains': ['24.a1.a1', '24.l1.a1', '36.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6744, 4399, 5084, 5480, 7362, 6159, 2807, 5352], 'generators': [2, 48, 4, 32], 'label': '288.630.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '72.46', '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': '24.14'}
  • id: 51646384
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.a1.b1', '6.e1.b1', '6.h1.b1'], 'contains': ['24.a1.b1', '24.l1.b1', '36.c1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6744, 4399, 3936, 525, 7362, 6159, 2577, 4346], 'generators': [77, 48, 4, 96], 'label': '288.630.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.c1.b1', '6.a1.b1'], 'normal_contains': ['24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646385
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.d1.b1', '24.f1.a1', '24.f1.b1', '24.j1.a1', '24.j1.b1', '36.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [448, -1, 4666, -1, 1143, -1, 9120, -1], 'generators': [1, 52, 48, 128], 'label': '288.630.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646386
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '36.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9538, -1, 2575, -1, 9372, -1, 1371, -1], 'generators': [52, 24, 32, 48], 'label': '288.630.12.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646387
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.b1', '6.e1.b1', '6.g1.b1'], 'contains': ['24.a1.b1', '24.g1.b1', '36.b1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9538, -1, 2016, -1, 9372, -1, 330, -1], 'generators': [3, 52, 96, 48], 'label': '288.630.12.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.e1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646388
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.a1', '6.f1.a1', '6.h1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '36.c1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7288, -1, 4871, -1, 6930, -1, 3034, -1], 'generators': [77, 48, 32, 4], 'label': '288.630.12.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646389
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 8, 'centralizer': '72.a1.a1', 'complements': ['144.d1.a1', '144.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.b1', '4.e1.a1', '6.e1.b1', '6.f1.a1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7847, 5530, 3919, 2516, 8012, 5802, 2768, 4732], 'generators': [77, 96, 32, 10, 4, 48], 'label': '288.630.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51646390
    {'ambient': '288.630', 'aut_centralizer_order': 96, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.b1', '6.f1.b1', '6.h1.b1'], 'contains': ['24.a1.b1', '24.k1.b1', '36.c1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7288, -1, 4148, -1, 6930, -1, 2161, -1], 'generators': [2, 48, 96, 4], 'label': '288.630.12.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.f1.b1', 'projective_image': '72.46', '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': '4.2'}
  • id: 51646391
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.a1.a1', '24.m1.a1', '24.m1.b1', '36.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5744, -1, 6186, -1, 5816, -1, 4801, -1], 'generators': [11, 48, 4, 32], 'label': '288.630.12.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '72.46', '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': '12.4'}
  • id: 51646392
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.b1', '6.g1.b1', '6.h1.b1'], 'contains': ['24.a1.b1', '24.m1.c1', '24.m1.d1', '36.d1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5744, -1, 5395, -1, 5816, -1, 4230, -1], 'generators': [11, 48, 4, 96], 'label': '288.630.12.g1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.g1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646393
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.n1.a1', '36.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7731, -1, 5609, -1, 5378, -1, 5031, -1], 'generators': [10, 48, 4, 32], 'label': '288.630.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '72.46', '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': '12.4'}
  • id: 51646394
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.b1', '6.e1.b1', '6.f1.b1'], 'contains': ['24.a1.b1', '24.n1.b1', '36.e1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7731, -1, 4458, -1, 5378, -1, 4460, -1], 'generators': [10, 48, 4, 96], 'label': '288.630.12.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.h1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51646395
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.o1.a1', '24.o1.b1', '36.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2693, -1, 8900, -1, 3384, -1, 6863, -1], 'generators': [11, 48, 4, 128], 'label': '288.630.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.i1.a1', 'projective_image': '72.46', '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': '6.1'}
  • id: 51646396
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.p1.a1', '24.p1.a2', '36.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2043, -1, 8686, -1, 2435, -1, 7322, -1], 'generators': [10, 48, 4, 128], 'label': '288.630.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.j1.a1', 'projective_image': '72.46', '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': '6.1'}
  • id: 51646397
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.c1.a1'], 'contains': ['24.i1.a1', '24.m1.a1', '24.n1.a1', '36.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4467, -1, 8326, -1, 4529, -1, 6403, -1], 'generators': [1, 10, 4, 32], 'label': '288.630.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646398
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.c1.a1'], 'contains': ['24.i1.a1', '24.m1.b1', '24.n1.a1', '36.f1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4467, -1, 8112, -1, 4529, -1, 6633, -1], 'generators': [49, 10, 4, 32], 'label': '288.630.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.k1.b1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646399
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.c1.b1'], 'contains': ['24.i1.b1', '24.m1.c1', '24.n1.b1', '36.f1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4467, -1, 7215, -1, 4529, -1, 5788, -1], 'generators': [1, 10, 4, 96], 'label': '288.630.12.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '12.k1.c1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646400
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.90180', 'aut_weyl_index': 4, 'centralizer': '72.a1.a1', 'complements': ['144.d1.a1', '144.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.g1.a1', '6.g1.b1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8281, 4146, 2553, 1644, 8484, 2467, 1254, 2049], 'generators': [3, 96, 32, 24, 4, 48], 'label': '288.630.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51646401
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.c1.b1'], 'contains': ['24.i1.b1', '24.m1.d1', '24.n1.b1', '36.f1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4467, -1, 7000, -1, 4529, -1, 6018, -1], 'generators': [49, 10, 4, 96], 'label': '288.630.12.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '12.k1.d1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646402
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1'], 'contains': ['24.j1.a1', '24.o1.a1', '24.p1.a1', '36.f1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [986, -1, 9952, -1, 1997, -1, 7092, -1], 'generators': [1, 10, 4, 128], 'label': '288.630.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.a1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646403
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1'], 'contains': ['24.j1.b1', '24.o1.a1', '24.p1.a2', '36.f1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [986, -1, 9640, -1, 1997, -1, 7552, -1], 'generators': [1, 10, 4, 224], 'label': '288.630.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.b1', 'projective_image': '144.154', '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': '6.1'}
  • id: 51646404
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.d1.a1'], 'contains': ['24.j1.a1', '24.o1.b1', '24.p1.a2', '36.f1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [986, -1, 9115, -1, 1997, -1, 8012, -1], 'generators': [49, 10, 4, 224], 'label': '288.630.12.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.c1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646405
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.d1.a1'], 'contains': ['24.j1.b1', '24.o1.b1', '24.p1.a1', '36.f1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [986, -1, 9427, -1, 1997, -1, 7782, -1], 'generators': [49, 10, 4, 128], 'label': '288.630.12.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.d1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51646406
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.h1.a1'], 'contains': ['24.k1.a1', '24.l1.a1', '24.m1.a1', '36.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6295, -1, 6736, -1, 6594, -1, 3695, -1], 'generators': [29, 2, 4, 32], 'label': '288.630.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.m1.a1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646407
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.h1.a1'], 'contains': ['24.k1.a1', '24.l1.a1', '24.m1.b1', '36.g1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6295, -1, 6569, -1, 6594, -1, 3821, -1], 'generators': [77, 2, 4, 32], 'label': '288.630.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.m1.b1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646408
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.h1.b1'], 'contains': ['24.k1.b1', '24.l1.b1', '24.m1.c1', '36.g1.a1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6295, -1, 6354, -1, 6594, -1, 3210, -1], 'generators': [29, 2, 4, 96], 'label': '288.630.12.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '12.m1.c1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646409
    {'ambient': '288.630', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.h1.b1'], 'contains': ['24.k1.b1', '24.l1.b1', '24.m1.d1', '36.g1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6295, -1, 6019, -1, 6594, -1, 3337, -1], 'generators': [77, 2, 4, 96], 'label': '288.630.12.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '12.m1.d1', 'projective_image': '144.154', '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': '12.4'}
  • id: 51646410
    {'ambient': '288.630', 'aut_centralizer_order': 576, 'aut_label': '16.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['32.a1.a1', '48.a1.a1', '48.a1.b1', '48.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2196, 5722, 1139, 5652, 511, 5224, 7673, 5871], 'generators': [52, 32, 96], 'label': '288.630.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '48.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646411
    {'ambient': '288.630', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.90180', 'aut_weyl_index': 4, 'centralizer': '72.a1.a1', 'complements': ['144.d1.a1', '144.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1', '4.g1.a1', '4.g1.b1', '6.h1.a1', '6.h1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6698, 7086, 5128, 3496, 6233, 819, 3659, 3803], 'generators': [77, 96, 32, 2, 48, 4], 'label': '288.630.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.c1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51646412
    {'ambient': '288.630', 'aut_centralizer_order': 576, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1'], 'contains': ['32.a1.a1', '48.b1.a1', '48.b1.b1', '48.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3949, 7096, 713, 3820, 2891, 3913, 4048, 3412], 'generators': [48, 32, 96], 'label': '288.630.16.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '48.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '144.148', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646413
    {'ambient': '288.630', 'aut_centralizer_order': 576, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.f1.a1', '8.g1.a1', '8.g1.b1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '48.c1.b1', '48.f1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3584, 8470, 7527, 2471, 3247, 2602, 5177, 2592], 'generators': [4, 32, 96], 'label': '288.630.16.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '48.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '144.154', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646414
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '48.g1.a1', '48.g1.b1', '48.h1.a1', '48.h1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1422, -1, 1740, -1, 868, -1, 9171, -1], 'generators': [1, 32, 96], 'label': '288.630.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.d1.a1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646415
    {'ambient': '288.630', 'aut_centralizer_order': 144, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.d1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '48.g1.c1', '48.g1.d1', '48.h1.c1', '48.h1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1422, -1, 1313, -1, 868, -1, 8796, -1], 'generators': [49, 32, 96], 'label': '288.630.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.d1.b1', 'projective_image': '288.630', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646416
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.b1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7667, -1, 2849, -1, 8088, -1, 1971, -1], 'generators': [1, 24], 'label': '288.630.18.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646417
    {'ambient': '288.630', 'aut_centralizer_order': 48, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.b1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.b1', '36.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7667, -1, 3408, -1, 8088, -1, 1561, -1], 'generators': [1, 2], 'label': '288.630.18.a1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.a1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646418
    {'ambient': '288.630', 'aut_centralizer_order': 32, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.c1.b1', '6.d1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.f1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5466, -1, 5364, -1, 4953, -1, 5565, -1], 'generators': [1, 10, 48], 'label': '288.630.18.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646419
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8765, -1, 3658, -1, 8358, -1, 1703, -1], 'generators': [2, 24], 'label': '288.630.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646420
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.f1.a1', '9.a1.a1'], 'contains': ['36.b1.b1', '36.c1.b1', '36.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8765, -1, 3540, -1, 8358, -1, 1830, -1], 'generators': [77, 10], 'label': '288.630.18.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51646421
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.g1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.b1.b1', '36.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8518, -1, 2619, -1, 8599, -1, 965, -1], 'generators': [3, 24], 'label': '288.630.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '72.46', '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': '8.5'}
  • id: 51646422
    {'ambient': '288.630', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '9.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7626, -1, 3652, -1, 7590, -1, 2563, -1], 'generators': [1, 32, 48, 2, 24, 52], 'label': '288.630.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51646423
    {'ambient': '288.630', 'aut_centralizer_order': 16, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.h1.b1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.c1.b1', '36.d1.a1', '36.g1.a1', '36.g1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8210, -1, 4930, -1, 7760, -1, 2368, -1], 'generators': [77, 2, 48], 'label': '288.630.18.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '72.46', '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': '8.5'}
  • id: 51646424
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6752, 4671, 4663, 5099, 6324, 6535, 4235, 5051], 'generators': [52, 48, 32], 'label': '288.630.24.a1.a1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.b1.a1', '48.c1.a1', '48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646425
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.b1', '12.b1.b1', '12.c1.b1', '12.e1.b1', '12.f1.b1', '12.g1.b1', '12.h1.b1'], 'contains': ['48.a1.b1', '48.b1.b1', '48.c1.b1', '72.a1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6752, 4671, 4147, 3024, 6324, 6535, 3861, 4231], 'generators': [52, 48, 96], 'label': '288.630.24.a1.b1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.a1', '12.a1.b1', '12.b1.b1', '12.c1.b1'], 'normal_contains': ['48.b1.b1', '48.c1.b1', '48.a1.b1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51646426
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': ['12.m1.d1', '12.m1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '72.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3336, 3297, 2048, 8420, 1224, 7846, 8983, 9644], 'generators': [1, 52, 32], 'label': '288.630.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646427
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': ['12.m1.a1', '12.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.b1'], 'contains': ['48.a1.b1', '48.g1.b1', '72.b1.a1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3336, 3297, 1376, 6689, 1224, 7846, 7860, 8824], 'generators': [1, 52, 96], 'label': '288.630.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.b1.a1', '12.a1.b1'], 'normal_contains': ['48.a1.b1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646428
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': ['12.m1.c1', '12.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.a1.a1'], 'contains': ['48.a1.a1', '48.g1.c1', '72.b1.b1'], 'core': '24.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3336, 3297, 1649, 9527, 1224, 7846, 8047, 7511], 'generators': [49, 52, 32], 'label': '288.630.24.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.c1', 'normal_contained_in': ['8.b1.b1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.c1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646429
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': ['12.m1.b1', '12.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.a1.b1'], 'contains': ['48.a1.b1', '48.g1.d1', '72.b1.b1'], 'core': '24.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3336, 3297, 685, 7554, 1224, 7846, 7299, 6691], 'generators': [49, 52, 96], 'label': '288.630.24.b1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.d1', 'normal_contained_in': ['8.b1.b1', '12.a1.b1'], 'normal_contains': ['48.a1.b1', '72.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.d1', 'projective_image': '144.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51646430
    {'ambient': '288.630', 'aut_centralizer_order': 1152, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.d1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.f1.a1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1807, -1, 5619, -1, 2293, -1, 7112, -1], 'generators': [52, 48, 128], 'label': '288.630.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '72.46', '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': '2.1'}
  • id: 51646431
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.h1.b1', '72.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [158, -1, 3777, -1, 155, -1, 9919, -1], 'generators': [1, 52, 128], 'label': '288.630.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '144.152', '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': '2.1'}
  • id: 51646432
    {'ambient': '288.630', 'aut_centralizer_order': 288, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.d1.a1'], 'contains': ['48.d1.a1', '48.h1.c1', '48.h1.d1', '72.b1.b1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [158, -1, 2957, -1, 155, -1, 9358, -1], 'generators': [49, 52, 128], 'label': '288.630.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.b1', 'projective_image': '144.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}